WIEN2k An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties

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1 WIEN2k An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties User s Guide, WIEN2k 14.2 (Release 10/15/2014) Peter Blaha Karlheinz Schwarz Georg Madsen Dieter Kvasnicka Joachim Luitz Vienna University of Technology Inst. of Physical and Theoretical Chemistry Getreidemarkt 9/156, A-1060 Vienna/Austria

2 Peter Blaha, Karlheinz Schwarz, Georg K. H. Madsen, Dieter Kvasnicka, Joachim Luitz: WIEN2k An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties revised edition WIEN2k 14.2 (Release 10/15/2014) Univ. Prof. Dr. Karlheinz Schwarz Techn. Universität Wien Institut für Physikalische und Theoretische Chemie Getreidemarkt 9/156 A-1060 Wien/Austria ISBN ISBN

3 Contents I Introduction to the WIEN2k package 1 1 Introduction 3 2 Basic concepts Density Functional Theory The APW Methods The LAPW Method The APW+lo Method General considerations Quick Start Naming conventions Starting the server Connecting to the w2web server Creating a new session Creating a new case Creating the struct file Initialization The SCF calculation The case.scf file Saving a calculation Calculating properties Electron density plots Density of States (DOS) X-ray spectra Bandstructure Bandstructure with band character plotting / full lines Volume Optimization Setting up a new case Manual setup Setting up a new case using w2web

4 II Detailed description of the files and programs of the WIEN2k package 31 4 Files and Program Flow Flow of input and output files Input/Output files The case.struct.file The case.scf file Flow of programs Core, semi-core and valence states Spin-polarized calculation Fixed-spin-moment (FSM) calculations Antiferromagnetic (AFM) calculations Spin-orbit interaction Orbital potentials Onsite-exact-exchange and hybrid functionals for correlated electrons Unscreened and screened hybrid functionals ( hf -module) modified Becke-Johnson potential (mbj) for band gaps DFT-D3 for dispersion energy Shell scripts Job control Main execution script (x lapw) Create the master input file case.struct (makestruct lapw) Job control for initialization (init lapw) Job control for iteration (run lapw or runsp lapw) Utility scripts Save a calculation (save lapw) Restoring a calculation (restore lapw) Reduce atomic spheres and interpolate density (reduce rmt lapw) Remove unnecessary files (clean lapw) Migrate a case to/from a remote computer (migrate lapw) Generate case.inst (instgen lapw) Set R-MT values in your case.struct file (setrmt lapw) create add atom clmsum lapw Create case.int file (for DOS) (configure int lapw) Check for running WIEN jobs (check lapw) Cancel (kill) running WIEN jobs (cancel lapw) Extract critical points from a Bader analysis (extractaim lapw) scfmonitor lapw

5 analyse lapw Check parallel execution (testpara lapw) Check parallel execution of lapw1 (testpara1 lapw) Check parallel execution of lapw2 (testpara2 lapw) grepline lapw initso lapw init hf lapw init mbj lapw vec2old lapw clmextrapol lapw makescratch lapw Structure optimization Lattice parameters (Volume, c/a, lattice parameters) Minimization of internal parameters (min lapw) Phonon calculations init phonon lapw analyse phonon lapw Parallel Execution k-point Parallelization MPI parallelization How to use WIEN2k as a parallel program The.machines file How the list of k-points is split Flow chart of the parallel scripts On the fine grained parallelization Chemical shift NMR calculations Introduction Options Additional notes Wannier functions (wien2wannier) Usage Help and FAQ Spontaneous Polarization, Piezoelectricity and Born Charges (BerryPI) Options Spontaneous Polarization Born effective charges Piezoelectric constants Getting on-line help

6 5.10 Interface scripts eplot lapw gibbs lapw parabolfit lapw dosplot lapw dosplot2 lapw Curve lapw specplot lapw rhoplot lapw prepare xsf lapw opticplot lapw addjoint-updn lapw Initialization NN Execution SGROUP Execution SYMMETRY Execution LSTART Execution Dimensioning parameters Input KGEN Execution Dimensioning parameters DSTART Execution Dimensioning parameters SCF cycle LAPW Execution Dimensioning parameters Input DFTD Execution Input

7 7.3 ORB Execution Dimensioning parameters Input HF Execution Input LAPW Execution Dimensioning parameters Input LAPWSO Execution Dimensioning parameters Input LAPW Execution Dimensioning parameters Input SUMPARA Execution Dimensioning parameters LAPWDM Execution Dimensioning parameters Input LCORE Execution Dimensioning parameters Input MIXER Execution Dimensioning parameters Input

8 8 Analysis, Properties and Optimization AIM Execution Dimensioning parameters Input BerryPI BROADENING Execution Input DIPAN Execution Dimensioning parameters Input ELAST Execution Input FILTVEC Execution Dimensioning parameters Input FSGEN IRelast IRREP Execution Dimensioning parameters JOINT Execution Dimensioning parameters Input KRAM Execution Dimensioning parameters Input LAPW Execution Dimensioning parameters LAPW Execution

9 Dimensioning parameters Input LAPW Execution Dimensioning parameters Input MINI Execution Dimensioning parameters Input NMR OPTIC Execution Dimensioning parameters Input OPTIMIZE Execution Input QTL Execution Input Output SPAGHETTI Execution Input TELNES Execution Input Practical considerations Files TETRA Execution Dimensioning parameters Input XSPEC Execution Dimensioning parameters Input

10 9 Utility Programs symmetso Execution pairhess Execution Dimensioning parameters Input eigenhess patchsymm Execution afminput Execution Dimensioning parameters clmcopy Execution Dimensioning parameters Input reformat hex2rhomb and rhomb in plane add columns clminter eosfit eosfit spacegroup join vectorfiles arrows xyz2struct cif2struct Tmaker struct2cif struct2poscar conv2prim fleur2wien StructGen of w2web supercell Execution structeditor

11 Execution Visualization BALSAC XCrysDen Unsupported software Examples TiC FCC Nickel Rutile supercell calc Further examples III Installation of the WIEN2k package and Dimensioning of programs Installation and Dimensioning Requirements Installation tips for mpich and fftw (either version or 3.3) Installation of WIEN2k Expanding the WIEN2k distribution Site configuration for WIEN2k User configuration Performance and special considerations Global dimensioning parameters w2web General issues How does w2web work? w2web-files in you home directory The configuration file conf/w2web.conf The password file conf/w2web.users Using the https-protocol with w2web Environment Variables Trouble shooting Ghost bands References 225

12 IV Appendix 231 A Local rotation matrices 233 A.1 Rutile (T io 2 ) A.2 Si Γ-phonon A.3 Trigonal Selenium B Periodic Table 237

13 List of Tables 4.1 Input and output files of init programs Input and output files of utility programs Input and output files of main programs in an SCF cycle Lattice type, description and bravais matrix used in WIEN2k. The angle γ is defined via cos(γ) = cos(γ ) sin(α) sin(β) + cos(β) cos(α) Relativistic quantum numbers XC shortcut-switches LM combinations of Cubic groups (3 (111)) direction, requires positive atomic index in case.struct. Terms that should be combined (Kara and Kurki-Suonio 81) must follow one another LM combination and local coordinate system of non-cubic groups (requires negative atomic index in case.struct) Possible values of QSPLIT and their interpretation Quantum numbers of the core state involved in the x-ray spectra

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15 List of Figures 2.1 Partitioning of the unit cell into atomic spheres (I) and an interstitial region (II) TiC in the sodium chloride structure. This plot was generated using BALSAC (see ). Interface programs between WIEN2k and BALSAC are available Startup screen of w2web Main window of w2web StructGen of w2web List of input files Task Electron Density Plots Electron density of TiC in (100) plane using Xcrysden Electron density of TiC in (100) plane Density of states of TiC Density of states of TiC Ti L III spectrum of TiC Bandstructure of TiC Bandstructure of TiC, showing t2g-character bands of Ti in character plotting mode Energy vs. volume curve for TiC Data flow during a SCF cycle (programx.def, case.struct, case.inx, case.outputx and optional files are omitted) Program flow in WIEN2k Flow chart of lapw1para Flow chart of lapw2para Schematic dependence of DOS and u l (r, E l ) on the energy D electron density in TiC generated with XCrysDen

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17 Licence conditions of WIEN2k P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka and J. Luitz Prof. Dr. Karlheinz Schwarz Vienna University of Technology Inst. of Physical and Theoretical Chemistry A-1060 Vienna, Getreidemarkt 9/156 AUSTRIA Fax: DEFINITIONS: In the following, the term the authors, refers to P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka and J. Luitz at the above address. Program shall mean that copyrighted APW+LO code (in source and object form) comprising the computer programs known as WIEN2k or the graphical user interface w2web. MANDATORY TERMS AND CONDITIONS: I will adhere to the following conditions upon receipt of the program: 1. All title, ownership and rights to the program or to copies of it remain with the authors, irrespective of the ownership of the media on which the program resides. 2. I will not supply a copy of the code to anyone for any reason whatsoever. This in no way limits my making copies of the code for backup purposes, or for running on more than one computer system at my institution (it is a site license for the registered group). I will refer any request for copies of the program to the authors. 3. I will not incorporate any part of WIEN2k or w2web into any other program system, without prior written permission of the authors. 4. I will keep intact all copyright notices. 5. I understand that the authors supply WIEN2k and w2web and its documentation on an as is basis without any warranty, and thus with no additional responsibility or liability. I agree to report any difficulties encountered in the use of WIEN2k or w2web to the authors. 6. In any publication in the scientific literature I will reference the program as follows: P. Blaha, K. Schwarz, G. K. H. Madsen, D. Kvasnicka and J. Luitz, WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Karlheinz Schwarz, Techn. Universität Wien, Austria), ISBN Please enter your publications with WIEN2k on our web-page for papers, so that we can easily include them in the list of WIEN-publications. In addition we like to receive a copy (ps-, pdf-file or reprint), especially for less common journals. Please send it to the second author, K. Schwarz. 7. It is understood that modifications of the WIEN2k or the w2web code can lead to problems where the authors may not be able to help. Please report useful modifications or major extensions to the authors. 8. I understand that support for running the program can not be provided in general, except on the basis of a joint project between the authors and the research partner. i

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19 Part I Introduction to the WIEN2k package 1

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21 1 Introduction The Linearized Augmented Plane Wave (LAPW) method has proven to be one of the most accurate methods for the computation of the electronic structure of solids within density functional theory. A full-potential LAPW-code for crystalline solids has been developed over a period of more than twenty years. A first copyrighted version was called WIEN and it was published by P. Blaha, K. Schwarz, P. Sorantin, and S. B. Trickey, in Comput. Phys. Commun. 59, 399 (1990). In the following years significantly improved and updated UNIX versions of the original WIENcode were developed, which were called WIEN93, WIEN95 and WIEN97. Now a new version, WIEN2k, is available, which is based on an alternative basis set. This allows a significant improvement, especially in terms of speed, universality, user-friendliness and new features. WIEN2k is written in FORTRAN 90 and requires a UNIX operating system since the programs are linked together via C-shell scripts. It has been implemented successfully on the following computer systems: Pentium systems running under Linux, IBM RS6000, HP, SGI, Compac DEC Alpha, and SUN. It is expected to run on any modern UNIX (LINUX) system. Hardware requirements will change from case to case (small cases with 10 atoms per unit cell can be run on any Pentium PC with 128 Mb under Linux), but generally we recommend a powerful PC or workstation with at least 256 Mb (better 512 Mb or more) memory and 1 Gb (better a few Gb) of disk space. For coarse grain parallization on the k-point level, a cluster of PCs with a 100 Mb/s network is sufficient. Faster communication is recommended for the fine grain (single k-point) parallel version. In order to use all options and features (such as the new graphical user interface w2web or some of its plotting tools) the following public domain program packages in addition to a F90 compiler must be installed: perl 5 or higher (for w2web only) emacs or another editor of your choice ghostscript (with jpg support) gnuplot (with png support) www-browser pdf-reader (acroread,...) MPI+SCALAPACK (on parallel computers only) Usually these packages should be available on modern systems. If one of these packages is not available, it can either be installed from public domain sources (see Chapt. 11) or the corresponding configuration may be changed (e.g. using vi instead of emacs). None of the principal components of WIEN2k requires these packages, only for advanced features or w2web they are needed. WIEN2k has the following features that are new with respect to WIEN97: 3

22 4 CHAPTER 1. INTRODUCTION due to the new APW+lo basis set it is significantly faster (up to an order of magnitude). Optimizations in the most time consuming parts of LAPW1 and LAPW2 have been made. iterative diagonalization (for cases with large matrices and few eigenvalues) beside the k-point parallelization (including heterogeneous workstation clusters) a fine grain parallelization based on MPI is also available. A new web-based graphical user interface w2web has been developed. It does NOT require an X-environment and thus WIEN2k can be controlled from (but not run on!) any Windows- PC. This should particularly help the novice to get acquainted with WIEN2k but it should be useful for the regular user as well. support for AFM and FSM calculations spin-orbit coupling, including a new p 1/2 -LO for higher accuracy wavefunction plotting determination of irreducible representations elastic constants (cubic cases only) Topological analysis based on Bader s atoms in molecules concept LDA+U, orbital polarization (OP), magnetic and electric fields Exact-exchange and Hybrid functionals inside spheres new PKZB and TPSS meta-gga functionals The development of WIEN2k was made possible by support from many sources. We try to give credit to all who have contributed. We hope not to have forgotten anyone who made an important contribution for the development or the improvement of the WIEN2k code. If we did, please let us know (we apologize and will correct it). The main developers in addition to the authors are the following groups: C. Ambrosch-Draxl (Univ. Graz, Austria) and her group, optics T. Charpin (Paris), elastic constants H. Hofstaetter and O.Koch (Vienna) iterative diagonalization M. Jamal (Iran) scripts, 2D-optimize K. Jorissen (Univ.Antwerp), C.Hebert (TU Wien), telnes3 R. Laskowski (TU Vienna), structeditor, main developer of mpi-parallelization, new dstart version, NMR module E. Kabliman (TU Vienna), arrows F. Karsai (TU Vienna), elast, lapwso D. Koller (TU Vienna), prepare xsf lapw L. Marks (Northwestern Univ.): speed-up, various optimizations, geometry optimization (PORT) and new mixer (MSEC1, MSR1, MSR1a) R. Luke (Univ. Delaware): new mixer (MSEC1) P. Novák and J. Kuneš (Prague), LDA+U, SO, lapwdm, qtl, dipan C. Persson (Uppsala), irreducible representations M. Scheffler (Fritz Haber Inst., Berlin) and his group, forces, dstart, geometry optimization E. Sjöstedt and L Nordström (Uppsala, Sweden), APW+lo J. Sofo and J. Fuhr (Barriloche), Bader analysis F. Tran (Vienna), various xc-functionals, Forces for orbital potential, Hybrid-Functionals P. Wissgott (TU Vienna) join vectorfiles B. Yanchitsky and A. Timoshevskii (Kiev), sgroup We want to thank those WIEN97 users, who reported bugs or made suggestions and thus contributed to new versions as well as persons who have made major contributions in the development of previous versions of the code: R. Augustyn (Vienna), U. Birkenheuer (Munich, wavefunction plotting), P. Blöchl (IBM Zürich), F. Boucher (Nantes), A. Chizmeshsya (Arizona), R.Dohmen and J.Pichlmeier (RZG Garching, parallelization) P. Dufek (Vienna), H. Ebert (Munich), E. Engel (Frankfurt), H.

23 Enkisch (Dortmund), M. Fähnle (MPI Stuttgart), B. Harmon (Ames, Iowa), S. Kohlhammer (Stuttgart), T. Kokalj (Ljubljana), H. Krimmel (Stuttgart), P. Louf (Vienna), I. Mazin (Washington), M. Nelhiebel (Vienna), V. Petricek (Prague), C. Rodrigues (La Plata, Argentina), P. Schattschneider (Vienna), R. Schmid (Frankfurt), D. Singh (Washington), H. Smolinski (Dortmund), T. Soldner (Leipzig), P. Sorantin (Vienna), S. Trickey (Gainesville), S. Wilke (Exxon, USA), B. Winkler (Kiel) 5

24 6 CHAPTER 1. INTRODUCTION This work was supported by the following institutions: Austrian Science Foundation (FWF-Projects P5939, P7063, P8176, SFB08-11) Siemens Nixdorf (WIEN93) IBM (WIEN) We take this opportunity to thank for all contributions. For suggestions or bug reports please contact the authors by

25 2 The basic concepts of the present band theory approach 2.1 The density functional theory An efficient and accurate scheme for solving the many-electron problem of a crystal (with nuclei at fixed positions) is the local spin density approximation (LSDA) within density functional theory (Hohenberg and Kohn 64, Kohn and Sham 65). Therein the key quantities are the spin densities ρ σ (r) in terms of which the total energy is E tot (ρ, ρ ) = T s (ρ, ρ ) + E ee (ρ, ρ )+ E Ne (ρ, ρ ) + E xc (ρ, ρ ) + E NN with E NN the repulsive Coulomb energy of the fixed nuclei and the electronic contributions, labelled conventionally as, respectively, the kinetic energy (of the non-interacting particles), the electron-electron repulsion, nuclear-electron attraction, and exchange-correlation energies. Two approximations comprise the LSDA, i), the assumption that E xc can be written in terms of a local exchange-correlation energy density µ xc times the total (spin-up plus spin-down) electron density as E xc = µ xc (ρ, ρ ) [ρ + ρ ]dr (2.1) and ii), the particular form chosen for that µ xc. Several forms exist in literature, we use the most recent and accurate fit to the Monte-Carlo simulations of Ceperly and Alder by Perdew and Wang 92. E tot has a variational equivalent with the familiar Rayleigh-Ritz principle. The most effective way known to minimize E tot by means of the variational principle is to introduce orbitals χ σ ik constrained to construct the spin densities as ρ σ (r) = i,k ρ σ ik χ σ ik(r) 2 (2.2) Here, the ρ σ ik are occupation numbers such that 0 ρσ ik 1/w k, where w k is the symmetry-required weight of point k. Then variation of E tot gives the Kohn-Sham equations (in Ry atomic units), [ 2 + V Ne + V ee + V σ xc]χ σ ik(r) = ɛ σ ikχ σ ik(r) (2.3) which must be solved and thus constitute the primary computational task. This Kohn-Sham equations must be solved self-consistently in an iterative process, since finding the Kohn-Sham orbitals requires the knowledge of the potentials which themselves depend on the (spin-) density and thus on the orbitals again. 7

26 8 CHAPTER 2. BASIC CONCEPTS Recent progress has been made going beyond the LSDA by adding gradient terms of the electron density to the exchange-correlation energy or its corresponding potential. This has led to the generalized gradient approximation (GGA) in various parameterizations, e.g. the one by Perdew et al 92 or Perdew, Burke and Ernzerhof (PBE) 96, which is the recommended option. A recent version called meta-gga by Perdew et al (1999) and Tao et al. (2003) employes for the evaluation of the exchange-correlation energy not only the gradient of the density, but also the kinetic energy density τ(r). Unfortunately, such schemes are not yet self-consistent. 2.2 The Full Potential APW methods Recently, the development of the Augmented Plane Wave (APW) methods from Slater s APW, to LAPW and the new APW+lo was described by Schwarz et al The LAPW method The linearized augmented plane wave (LAPW) method is among the most accurate methods for performing electronic structure calculations for crystals. It is based on the density functional theory for the treatment of exchange and correlation and uses e.g. the local spin density approximation (LSDA). Several forms of LSDA potentials exist in the literature, but recent improvements using the generalized gradient approximation (GGA) are available too (see sec. 2.1). For valence states relativistic effects can be included either in a scalar relativistic treatment (Koelling and Harmon 77) or with the second variational method including spin-orbit coupling (Macdonald 80, Novák 97). Core states are treated fully relativistically (Desclaux 69). A description of this method to linearize Slater s old APW method (i.e. the LAPW formalism) and further programming hints are found in many references: Andersen 73, 75, Koelling 72, Koelling and Arbman 75, Wimmer et al. 81, Weinert 81, Weinert et al. 82, Blaha and Schwarz 83, Blaha et al. 85, Wei et al. 85, Mattheiss and Hamann 86, Jansen and Freeman 84, Schwarz and Blaha 96). An excellent book by D. Singh (Singh 94) describes all the details of the LAPW method and is highly recommended to the interested reader. Here only the basic ideas are summarized; details are left to those references. Like most energy-band methods, the LAPW method is a procedure for solving the Kohn-Sham equations for the ground state density, total energy, and (Kohn-Sham) eigenvalues (energy bands) of a many-electron system (here a crystal) by introducing a basis set which is especially adapted to the problem. Figure 2.1: Partitioning of the unit cell into atomic spheres (I) and an interstitial region (II) This adaptation is achieved by dividing the unit cell into (I) non-overlapping atomic spheres (centered at the atomic sites) and (II) an interstitial region. In the two types of regions different basis sets are used:

27 2.2. THE APW METHODS 9 1. (I) inside atomic sphere t, of radius R t, a linear combination of radial functions times spherical harmonics Y lm (r) is used (we omit the index t when it is clear from the context) φ kn = [A lm,kn u l (r, E l ) + B lm,kn u l (r, E l )]Y lm (ˆr) (2.4) lm where u l (r, E l ) is the (at the origin) regular solution of the radial Schroedinger equation for energy E l (chosen normally at the center of the corresponding band with l-like character) and the spherical part of the potential inside sphere t; u l (r, E l ) is the energy derivative of u l evaluated at the same energy E l. A linear combination of these two functions constitute the linearization of the radial function; the coefficients A lm and B lm are functions of k n (see below) determined by requiring that this basis function matches (in value and slope) each plane wave (PW) the corresponding basis function of the interstitial region; u l and u l are obtained by numerical integration of the radial Schroedinger equation on a radial mesh inside the sphere. 2. (II) in the interstitial region a plane wave expansion is used φ kn = 1 ω e ikn r (2.5) where k n = k + K n ; K n are the reciprocal lattice vectors and k is the wave vector inside the first Brillouin zone. Each plane wave is augmented by an atomic-like function in every atomic sphere. The solutions to the Kohn-Sham equations are expanded in this combined basis set of LAPW s according to the linear variation method ψ k = n c n φ kn (2.6) and the coefficients c n are determined by the Rayleigh-Ritz variational principle. The convergence of this basis set is controlled by a cutoff parameter R mt K max = 6-9, where R mt is the smallest atomic sphere radius in the unit cell and K max is the magnitude of the largest K vector in equation (2.6). In order to improve upon the linearization (i.e. to increase the flexibility of the basis) and to make possible a consistent treatment of semicore and valence states in one energy window (to ensure orthogonality) additional (k n independent) basis functions can be added. They are called local orbitals (LO) (Singh 91) and consist of a linear combination of 2 radial functions at 2 different energies (e.g. at the 3s and 4s energy) and one energy derivative (at one of these energies): φ LO lm = [A lm u l (r, E 1,l ) + B lm u l (r, E 1,l ) + C lm u l (r, E 2,l )]Y lm (ˆr) (2.7) The coefficients A lm, B lm and C lm are determined by the requirements that φ LO should be normalized and has zero value and slope at the sphere boundary The APW+lo method Sjöstedt, Nordström and Singh (2000) have shown that the standard LAPW method with the additional constraint on the PWs of matching in value AND slope to the solution inside the sphere is not the most efficient way to linearize Slater s APW method. It can be made much more efficient when one uses the standard APW basis, but of course with u l (r, E l ) at a fixed energy E l in order to keep the linear eigenvalue problem. One then adds a new local orbital (lo) to have enough variational flexibility in the radial basisfunctions: φ kn = [A lm,kn u l (r, E l )]Y lm (ˆr) (2.8) lm

28 10 CHAPTER 2. BASIC CONCEPTS φ lo lm = [A lm u l (r, E 1,l ) + B lm u l (r, E 1,l )]Y lm (ˆr) (2.9) This new lo (denoted with lower case to distinguish it from the LO given in equ. 2.7) looks almost like the old LAPW -basis set, but here the A lm and B lm do not depend on k n and are determined by the requirement that the lo is zero at the sphere boundary and normalized. Thus we construct basis functions that have kinks at the sphere boundary, which makes it necessary to include surface terms in the kinetic energy part of the Hamiltonian. Note, however, that the total wavefunction is of course smooth and differentiable. As shown by Madsen et al. (2001) this new scheme converges practically to identical results as the LAPW method, but allows to reduce RKmax by about one, leading to significantly smaller basis sets (up to 50 %) and thus the corresponding computational time is drastically reduced (up to an order of magnitude). Within one calculation a mixed LAPW and APW+lo basis can be used for different atoms and even different l-values for the same atom (Madsen et al. 2001). In general one describes by APW+lo those orbitals which converge most slowly with the number of PWs (such as TM 3d states) or the atoms with a small sphere size, but the rest with ordinary LAPWs. One can also add a second LO at a different energy so that both, semicore and valence states, can be described simultaneously General considerations In its general form the LAPW (APW+lo) method expands the potential in the following form V LM (r)y LM (ˆr) LM V (r) = V K e ik r K inside sphere outside sphere (2.10) and the charge densities analogously. Thus no shape approximations are made, a procedure frequently called a full-potential method. The muffin-tin approximation used in early band calculations corresponds to retaining only the l = 0 component in the first expression of equ and only the K = 0 component in the second. This (much older) procedure corresponds to taking the spherical average inside the spheres and the volume average in the interstitial region. The total energy is computed according to Weinert et al. 82. Rydberg atomic units are used except internally in the atomic-like programs (LSTART and LCORE) or in subroutine outwin (LAPW1, LAPW2), where Hartree units are used. The output is always given in Rydberg units. The forces at the atoms are calculated according to Yu et al (91). For the implementation of this formalism in WIEN see Kohler et al (96) and Madsen et al An alternative formulation by Soler and Williams (89) has also been tested and found to be equivalent, both in computationally efficiency and numerical accuracy (Krimmel et al 94). The Fermi energy and the weights of each band state can be calculated using a modified tetrahedron method (Blöchl et al. 94), a Gaussian or a temperature broadening scheme. Spin-orbit interactions can be considered via a second variational step using the scalar-relativistic eigenfunctions as basis (see Macdonald 80, Singh 94 and Novák 97). In order to overcome the problems due to the missing p 1/2 radial basis function in the scalar-relativistic basis (which corresponds to p 3/2 ), we have recently extended the standard LAPW basis by an additional p 1/2 -local orbital, i.e. a LO with a p 1/2 basis function, which is added in the second-variational SO calculation (Kuneš et al. 2001).

29 2.2. THE APW METHODS 11 It is well known that for localized electrons (like the 4f states in lanthanides or 3d states in some TM-oxides) the LDA (GGA) method is not accurate enough for a proper description. Thus we have implemented various forms of the LDA+U method as well as the Orbital polarization method (OP) (see Novák 2001 and references therein). In addition you can also calculate exact-exchange inside the spheres and apply various hybrid functionals (see Tran et al for details). One can also consider interactions with an external magnetic (see Novák 2001) or electric field (via a supercell approach, see Stahn et al. 2000). PROPERTIES: The density of states (DOS) can be calculated using the modified tetrahedron method of Blöchl et al. 94. X-ray absorption and emission spectra are determined using Fermi s golden rule and dipole matrix elements (between a core and valence or conduction band state respectively). (Neckel et al. 75, Schwarz et al 79,80) X-ray structure factors are obtained by Fourier Transformation of the charge density. Optical properties are obtained using the Joint density of states modified with the respective dipole matrix elements according to Ambrosch et al. 95, Abt et al. 94, Abt 97. and in particular Ambrosch 06. A Kramers-Kronig transformation is also possible. An analysis of the electron density according to Bader s atoms in molecules theory can be made using a program by J. Sofo and J. Fuhr (2001)

30 12 CHAPTER 2. BASIC CONCEPTS

31 3 Quick Start Contents 3.1 Naming conventions Starting the server Connecting to the w2web server Creating a new session Creating a new case Creating the struct file Initialization The SCF calculation The case.scf file Saving a calculation Calculating properties Setting up a new case We assume that WIEN2k is properly installed and configured for your site and that you ran userconfig lapw to adjust your path and environment. (For a detailed description of the installation see chapter 11. This chapter is intended to guide the novice user in the handling of the program package. We will use the example of TiC in the sodium chloride structure to show which steps are necessary to initialize a calculation and run a self consistent field cycle. We also demonstrate how to calculate various physical properties from these SCF data. Along the way we will give all important information in a very abridged form, so that the novice user is not flooded with information, and the experienced user will be directed to more complete information. In this chapter we will also show, how the new graphical user interface w2web can be utilized to setup and run the calculations. 3.1 Naming conventions Before we begin with our introductory example, we describe the naming conventions, to which we will adhere throughout this user s guide. On UNIX systems the files are specified by case.type and it is required that all files reside in a subdirectory./case. Here and in the following sections and in the shell scripts which run the package themselves, we follow a simple, systematic convention for file labeling. For the general discussion (when no specific crystal is involved), we use case, while for a specific case, e.g. TiC, we use the following notation: 13

32 14 CHAPTER 3. QUICK START Figure 3.1: TiC in the sodium chloride structure. This plot was generated using BALSAC (see ). Interface programs between WIEN2k and BALSAC are available. case=tic The filetype type always describes the content of the file (e.g., type=inm is input for mixer). Thus the input to MIXER for TiC is found in the file TiC.inm which should be in subdirectory./tic. 3.2 Starting the w2web server Start the user interface w2web on the computer where you want to execute WIEN2k(you may have to telnet, ssh,.. to this machine) with the command w2web [-p xxxx] If the default port (7890) used to serve the interface is already in use by some other process, you will get the error message w2web failed to bind port port already in use!. Then you will have to choose a different port number (between 1024 and 65536). Please remember this port number, you need it when connecting to the w2web server. Note: Only user root can specify port numbers below 1024! At the first startup of this server, you will also be asked to setup a username and password, which is required to connect to this server.

33 3.3. CONNECTING TO THE W2WEB SERVER Connecting to the w2web server Use your favorite WWW-browser to connect to w2web, specifying the correct portnumber, e.g. netscape where w2web runs:7890 (If you do not remember the portnumber, you can find it by using ps -ef grep w2web on the computer where w2web is running.) You should see a screen as in Fig Creating a new session The user interface w2web uses sessions to distinguish between different working environments and to quickly change between different calculations. First you have to create a new session (or select an old one). Enter TiC and click the Create button. Note: Creating a session does not automatically create a new directory! You will be placed in your home directory if no working directory was designated to this session previously (or if the directory does not exist any more). Figure 3.2: Startup screen of w2web

34 16 CHAPTER 3. QUICK START 3.5 Creating a new case-directory Using Session Mgmt. change directory you can select an existing directory or create a new one. For this example create a new directory lapw and than TiC using the Create button. After the directory has been created, you have to click on select current directory to assign this newly created directory to the current session. After clicking on Click to restart session the main window of w2web will appear (Fig.3.3. Figure 3.3: Main window of w2web 3.6 Creating the master input file case.struct To create the file TiC.struct start the struct-file generator using Execution StructGen (see figure 3.4). For a new case w2web creates an empty structure template in which you can specify structural data. Later on this information is used to generate the TiC.struct file. As a first step specify the number of atoms (2 for TiC) and fill in the data given below into the corresponding fields (white boxes): Title TiC Lattice F (for face centered) a Å(make sure the Ang button is selected) b Å c Å α, β, γ 90 Atom Ti, enter position (0,0,0) Atom C, enter position (.5,.5,.5) Click Save Structure (Z will be updated automatically) and set automatically RMT and continue editing :

35 3.6. CREATING THE STRUCT FILE 17 This will compute the nearest neigbor distances using the program nn and setrmt lapw will then determine the optimal RMT values (muffin-tin radius, atomic sphere radius). To learn more about the philosophy of setting RMTs see Since it is essential to keep RMTs constant within a series of calculations (eg. when you do a Volumeoptimization, see ), you should already now decide whether you want to do just one single calculation with fixed structural parameters, or whether you intend a relaxation of internal parameters (using forces and min lapw) or a volume optimization, which would required reduced RMT values. Choose a reduction of 3 % so that we can later optimize the lattice parameter. Figure 3.4: StructGen of w2web When you are done, exit the StructGen with save file and clean up. This will generate the file TiC.struct (shown now in view-only mode with a different background color), which is the master input file for all subsequent programs. A few other hints on StructGen: You have to click on Save Structure after every modifications you make in the white fields.

36 18 CHAPTER 3. QUICK START Add/remove a position/atom only if you have made no other changes before. In a face-centered (body-centered) spacegroup you have to enter just one atom (not the ones in (.5,.5,0),... ). StructGen offers a built in calculator: Each position of equivalent atoms can be entered as a number, a fraction (e.g. 1/3) or a simple expression (e.g /3). The first position defines the variables x, y and z, which can be using in expression defining the other positions (e.g. y, x, z + 1/2). When you now choose Files show all files, you will see, that tic.struct has been created. For a detailed description of these files consult sections 4.3 and Initialization of the calculation (init lapw) After the basic input file has been created, initalization of the calculation is done by Execution initialize calc.. For structures given by experiment (not man-made supercells,...) you would usually run in Fast mode, just specify a few most important imput parameters (or use the defaults). However, this introduction will guide you through all individual steps necessary to initialite the calculation. Simply follow the steps that are highlighted in green and follow the instructions. The initialization process is described in detail in section Alternatively you could run the script init lapw [-b] from the command line. All actions of this script are logged in short in :log and in detail in the file case.dayfile, which can easily be accessed by Utils. show dayfile. Initializing the calculation will run several steps automatically, where x is the script to start WIEN2k programs (see section: 5.1.1). x nn calculates the nearest neighbors up to a specified distance and thus helps to determine the atomic sphere radii (you must specify a distance factor f, e.g. 2, and all distances up to f * NN-dist. are calculated) view TiC.outputnn : check for overlapping spheres, coordination numbers and nearest neighbor distances, (e.g. in the sodium chloride structure there must 6 nearest and 12 next nearest neighbors). Using these distances and coordinations you can check whether you put the proper positions into your struct file or if you made a mistake. nn also checks whether your equivalent atoms are really crystallographically equivalent and eventually writes a new struct-file which you may or may not accept. If you have not done so at the very beginning, go back to StructGen and choose proper RMT values. You can save a lot of CPU-time by changing RMT to almost touching spheres. See Sec.4.3 x sgroup calculates the point and spacegroups for the given structure view TiC.outputsgroup : Now you can either accept the TiC.struct file generated by sgroup (if you want to use the spacegroup information or a different cell has been found by sgroup) or keep your original file (default). x symmetry generates from a raw case.struct file the space group symmetry operations, determines the point group of the individual atomic sites, generates the LM expansion for the lattice harmonics (in case.in2 st) and local rotation matrices (in case.struct st). view TiC.outputs : check the symmetry operations (they have been written to or compared with already available ones in TiC.struct by the program symmetry) and the point group symmetry of the atoms (You may compare them with the International Tables for X-Ray Crystallography ). If the output does not match your expectations from the Tables, you might have made an error in specifying the positions. The TiC.struct file will be updated with symmetry operations, positive or negativ atomic counter (for cubic point group symmetries) and the local rotation matrix.

37 3.7. INITIALIZATION 19 instgen lapw : You are requested to generate an input file TiC.inst and can define the spinpolarization of each atom. While this is not important for TiC, it is very important for spinpolarized calculations and in particular for anti-ferromagnetic cases, where you should flip the spin of the AFM atoms and/or set the spin of the non-magnetic atoms (eg. oxygen in NiO) to zero. x lstart generates atomic densities (see section 6.4) and determines how the orbitals are treated in the band structure calculations (i.e. as core or band states, with or without local orbitals,... ). You are requested to specify the desired exchange correlation potential and an energy that separates valence from core states. For TiC select the recommended potential option GGA of Perdew-Burke-Ernzerhof 96 and a separation energy of -6.0 Ry. edit TiC.outputst : check the output (did you specify a proper atomic configuration, did lstart converge, are the core electrons confined to the atomic sphere?). Warnings for the radial mesh can usually be neglected since it affects only the atomic total energy. lstart generates TiC.in0 st, in1 st, in2 st, inc st and inm st. For Ti it selects automatically 1s, 2s, and 2p as core states, 3s and 3p will be treated with local orbitals together with 3d, 4s and 4p valence states. edit TiC.in1 st : As mentioned, the input files are generated automatically with some default values which should be a reasonable choice for most cases. Nevertheless we highly recommend that you go through these inputs and become familiar with them. The most important parameter here is RKMAX, which determines the number of basis functions (size of the matrices). Values between 5-9 (3 if you have small H-spheres) are usually reasonable. Eventually you could change here the usage of APW or LAPW (set 1 or 0 after the CONT/STOP switch), since often APW is necessary only for orbitals more difficult to converge (3d, 4f). Here we will just change EMAX of the energy window from 1.5 to 2.0 Ry in order to be able to calculate the unoccupied DOS to higher energies. edit TiC.in2 st : Here you may limit(increase the LM expansion, increasse the value of GMAX (in cases with small spheres (e.g. systems with H-atoms) it will be automatically increased anyway) or specify a different BZ-integration method to determine the Fermi energy. For this example you should not change anything so that you can compare your results with the test run. Copy all generated inputs (from case.in st to case.in*). In cases without inversion symmetry the files case.in1c, in2c are produced. x kgen generates a k-mesh in the Brillouin zone (BZ). You must specify the number of k-points in the whole BZ (use 1000 for comparison with the provided output, a good calculation needs 10 times as much). For details see section 6.5. view TiC.klist : check the number of k-points in the irreducible wedge of the BZ (IBZ) and the energy interval specified for the first k-point. You can now either rerun kgen (and generate a different k-mesh) or continue. x dstart generates a starting density for the SCF cycle by superposition of atomic densities generated in lstart. For details see section 6.6. view TiC.outputd (check if gmax >gmin) Now you are asked, whether or not you want to run a spin-polarized calculation (in such a case case dstart is re-run to generate spin-densities). For TiC say No. Alternatively, w2web provides a Fast-mode, which is the recommended default and where the most imortant inputs can be specified right at the beginning and then the whole initialization runs at once. Please check carefully the STDOUT-listing and some output-files for possible errors or warnings!!. Only for hand-made case.struct files (eg. using supercells,...) one should run the first steps (from nn to symmetry step by step, since in such cases these programs may rewrite case.struct and specify different multiplicities or even change the unit cell. Initialization of a calculation (running init lapw) will create all inputs for the subsequent SCF calculation choosing some default options and values. You can find a list of input files using Files input files ( 3.5).

38 20 CHAPTER 3. QUICK START Figure 3.5: List of input files 3.8 The SCF calculation After the case has been set up, a link to run SCF is added, ( Run Programs run SCF and you should invoke the self-consistency cycle (SCF). This runs the script run lapw with the desired options. The SCF cycle consists of the following steps: LAPW0 (POTENTIAL) generates potential from density LAPW1 (BANDS) calculates valence bands (eigenvalues and eigenvectors) LAPW2 (RHO) computes valence densities from eigenvectors LCORE computes core states and densities MIXER mixes input and output densities After selecting run SCF from the Execution menu, the SCF-window will open, and you can now specify additional parameters. For this example we select charge convergence to : Specify charge to be used as convergence criterion, and select a value of (-cc ). To run the SCF cycle, click on Run! Since this might take a long time for larger systems; you can specify the Execution type to be batch or submit (if your system is configured with a queuing system and w2web has been properly set up, see section 11.3). While the calculation is running (as indicated by the status frame in the top right corner of the window), you can monitor several quantities (see section 3.9). Once the calculation is finished (11 iterations), view case.dayfile for timing and errors and compare your results with the files in the provided example (TiC/case scf).

39 3.9. THE CASE.SCF FILE 21 For magnetic systems you would run a spin-polarized calculation with the script runsp lapw. The program flow of such a calculation is described in section and the script itself in section The history file case.scf During the SCF cycle the essential data of each iteration are appended to the file case.scf, in our example TiC.scf. For an easier retrieval of certain quantities, the essential lines carry a label of the form :LABEL: which can be used to monitor these quantities during a SCF run. The information is retrieved using the UNIX grep command or using the Utils. analyze menu. While the SCF cycle of TiC is running try to monitor e.g. the total energy (label :ENE) or the charge distance (label :DIS). The calculation has converged, when the convergence criterion is met for three subsequent iterations (compare the charge distance in the example). For a detailed description of the various labels consult section Saving a calculation Before you proceed to another calculation, you should save the results of the SCF-cycle with the save lapw command, which is also described in detail in section This can also be done from the graphical user interface by choosing the Utils. save lapw menu. Save the result to this example under the name TiC scf. You can now improve your calculation and check the convergence of the most important parameters: increase RKMAX and GMAX in case.in1 and case.in2 increase the k-mesh with x kgen choose a different exchange-correlation potential in case.in0 Then just execute another run lapw using Execution run SCF Calculating properties Once the SCF cycle has converged one can calculate various properties like Density of States (DOS), band structure, Optical properties or X-ray spectra. For the calculation of properties (which from now on will be called Tasks ). We strongly encourage the user to utilize the user interface, w2web. This user interface automatically supplies input file templates and shows how to calculate the named properties on a step by step basis Electron density plots Select El. Dens. from the Tasks menu and click on the buttons one by one (see figure 3.6): The total charge density includes the Ti 3s and 3p states and the resulting density around Ti would be very large and dominated by these semicore states. To get a meaningful picture of the chemical bonding effects one must remove these states. Inspection of TiC.scf1 and TiC.scf2 should allow you to select an EMIN value to eliminate the Ti 3s and 3p semicore states.

40 22 CHAPTER 3. QUICK START Figure 3.6: Task Electron Density Plots Recalculate the valence density with EMIN=-1.0 to truncate Ti 3s and 3p (x lapw2). This is only possible, when you still have a valid TiC.vector file on a tetrahedral mesh. Select a plane and plot the density in the (100) plane of TiC. When XCRYSDEN is installed (for details see it will be offered automatically and provides a convenient way to specify a plane and create a colorful plot 3.7. Select 2D-plot Specify a resolution of 100 points (first line) Select a plane by selecting 3 atoms and define these 3 atoms by clicking on them. Choose rectangular parallelogram and enlarge the rectangular selection by 0.5 (for all 4 margins, then update the display) calculate the density and produce a nice contour plot: choose rainbow -colors, activate all display-option buttens, and choose in Ranges a smaller highest rendered value. Finally, use smaller spheres (pipe+ball display model) and thinner bonds (Modify/Ball-Stick-ratio). Alternatively, without XCRYSDEN, edit TiC.in5 and choose the offered template input file. To select the (100) plane for plotting specify the following input: # origin of plot (x,y,z,denominator) # x-end of plot # y-end of plot # x,y,z number of shells # x, y plotting mesh, choose ratio similar to x,y length RHO ANG VAL NODEBUG

41 3.11. CALCULATING PROPERTIES 23 ORTHO For a detailed description of input options consult section Calculate electron density (x lapw5) Plot output (using rhoplot), after the first preview select a range zmin=-0.5 to zmax=2 Figure 3.7: Electron density of TiC in (100) plane using Xcrysden Compare the result with the electron density plotted in the (100) plane (see figure 3.8). The program gnuplot (public domain) must be installed on your computer. For more advanced graphics use your favorite plotting package or specify other options in gnuplot (see rhoplot lapw how gnuplot is called).

42 24 CHAPTER 3. QUICK START Figure 3.8: Electron density of TiC in (100) plane Density of States (DOS) Select Density of States (DOS) from the Tasks menu and click on the buttons one by one: Calculate partial charges (x lapw2 -qtl). (This is only possible, when you still have a valid TiC.vector file on a tetrahedral mesh.) Create TiC.int, either using configure TiC.int or/and by editing the offered template input file. Select: total DOS, Ti-d, Ti-d eg, Ti-d t2g, C-s and C-p-like DOS. TiC EMIN, DE, EMAX, Gauss-broadening 6 NUMBER OF DOS-CASES 0 1 tot (atom,case,description) 1 4 Ti d 1 5 Ti eg 1 6 Ti t2g 2 2 C s 2 3 C p For a detailed description of input options consult section Calculate DOS (x tetra). Preview output using dosplot If you want to use the supplied plotting interface dosplot2 to preview the results, the program gnuplot (public domain) must be installed on your computer. The calculated DOS can be compared with figures 3.9 and Together with the electron density the partial DOS allows you to analyse the chemical bonding (covalency between T i d eg and C p, non-bonding T i d t2g, charge transfer estimates,...)

43 3.11. CALCULATING PROPERTIES 25 Figure 3.9: Density of states of TiC Figure 3.10: Density of states of TiC

44 26 CHAPTER 3. QUICK START X-ray spectra Select X-Ray Spectra from the Tasks menu and click on the buttons one by one: Calculate partial charges (x lapw2 -qtl). This is only possible, when you still have a valid TiC.vector file on a tetrahedral mesh. To reproduce this figure you will have to increase the EMAX value in your TiC.in1 to 2.5 Ry and rerun x lapw1 Edit TiC.inxs; choose the offered template. This template will calculate the L III - spectrum of the first atom (Ti in this example) in the energy range between -2 and 15 ev. For a detailed description of the contents of this input file refer to section Calculate spectra Preview spectra If you want to use the supplied plotting interface specplot to preview the results, the public domain program gnuplot must be installed on your computer. The calculated TiC Ti-L III -spectrum can be compared with figure Figure 3.11: Ti L III spectrum of TiC Bandstructure Select Bandstructure from the Tasks menu and click on the buttons one by one: Create the file TiC.klist band from the template in $WIENROOT/SRC templates/fcc.klist. (To calculate a bandstructure a special k-mesh along high symmetry directions is necessary. For a few crystal structures template files are supplied in the SRC-directory, you can also use XCRYSDEN (save it as xcrysden.klist) to generate a k-mesh or type in your own mesh. Calculate Eigenvalues using the -band switch (which changes lapw1.def such that the k-mesh is read from TiC.klist band and not from TiC.klist) Note: When you want to calculate DOS, charge densities or spectra after this bandstructure, you must first recalculate the TiC.vector file using the tetrahedral k-mesh, because the k-mesh for the band structure plots is not suitable for calculations of such properties.

45 3.11. CALCULATING PROPERTIES 27 Edit TiC.insp: insert the correct Fermi energy (which can be found in the saved scf-file) and specify plotting parameters. For comparison with figure 3.12 select an energy-range from -13 to 8 ev. Calculate Bandstructure (x spaghetti). Preview Bandstructure (needs ghostscript installed). If you want to preview the bandstructure, the program ghostview (public domain) must be installed on your computer. You can compare your calculated bandstructure with figure Figure 3.12: Bandstructure of TiC Bandstructure with band character plotting / full lines Select again Bandstructure from the Tasks menu. We assume that you have already done the steps described in the previous section (generate TiC.klist band and x lapw1 -band). Calculate partial charges (x lapw2 -qtl -band) Note: You have to calculate the partial charges for the new special k-mesh specified above and cannot use the partial charges from the DOS calculation. Edit TiC.insp: insert the correct Fermi energy (same as before) and specify plotting parameters. For band character plotting (see figure 3.13) select line type = dots and jatom=1, jtype=6 and jsize=0.2 (in the last input line) to produce a character plot of the Ti t2g-like character bands. Calculate Bandstructure (x spaghetti) Preview Bandstructure To plot the bandstructure with full lines, calculate the irreducible representations with x irrep and select lines in case.insp. If you have case.irrep* or case.qtl* files from previous runs which do not fit to the present case.output1 file, you may get errors while running spaghetti. In this case remove all case.irrep or case.qtl files. You can compare your results with figure 3.13.

46 28 CHAPTER 3. QUICK START Figure 3.13: Bandstructure of TiC, showing t2g-character bands of Ti in character plotting mode Volume Optimization Select Optimize (V,c/a) from the Execution menu. Setup the shell script optimize.job script using x optimize and volume variations of -10, -5, 0, +5 and +10%. Then run the optimize.job. When the job has finished, you should click on Plot and then preview the energy curve. You should get an energy curve as in figure On the screen you will find the fitting parameters for the equation of states (Murnaghan, Birch-Murnaghan and the EOS2 equation, see sec. 9.12). This information is also written to TiC.outputeos. Figure 3.14: Energy vs. volume curve for TiC

47 3.12. SETTING UP A NEW CASE Setting up a new case In order to setup a new case you need at least the following information: The lattice parameters (in Bohr or Ångstroms) and angles, the lattice type (primitive, face-centered, hexagonal,...) or spacegroup, the position of all equivalent and inequivalent atoms in fractions of the unit cell. Alternatively with the new StructGen you can specify the spacegroup and only the inequivalent positions. The equivalent ones will be generated automatically. Usually this information can be collected from the International Tables of Crystallography once you know the space group, the Wyckoff position and the internal free coordinates Manually setting up a new case Usually for a new case the input is not created by hand, but using some utilities. We recommend the script makestruct lapw which will ask for the required input and create init.struct, which you should copy to case.struct. Alternatively, you can use cif2struct or xyz2struct to convert a cif, txt or xyz file into the WIEN2k case.struct file. Check page 196 for more info on the specific file formats. You can also use the struct file from a similar case as pattern, but note, that the automatic setting of proper R0-values is not guaranteed by that procedure and you should use it only for VERY SIMILAR cases (elements). Change into the lapw subdirectory and proceed as follows: mkdir case new cd case new cp../case old/case old.struct case new.struct Now edit case new.struct (see section 4.3) as necessary (Note: this is a fixed formatted file, so all values must remain at their proper columns). Afterwards generate case new.inst using instgen lapw Setting up a new case using w2web Use the menu Session Mgmt. change session of w2web to create a new session (enter the name of the new session and click on Create ). Then you should also create a new directory and select it.. When you select Execution StructGen, you have several choices: You can just specify the number of non-equivalent atoms and a template file will be created. In StructGen you simply specify the lattice (type or spacegroup), cell parameters and name and positions of atoms. When you save file and clean up the new case.struct file and the case.inst file are created automatically. Alternatively, you can use cif2struct or xyz2struct to convert a cif, txt or xyz file into the WIEN2k case.struct file. Check page 196 for more info on the specific file formats. For more information on the StructGen refer to page 198.

48 30 CHAPTER 3. QUICK START

49 Part II Detailed description of the files and programs of the WIEN2k package 31

50

51 4 File structure and program flow Contents 4.1 Flow of input and output files Input/Output files The case.struct.file The case.scf file Flow of programs (for naming conventions see section 3.1) 4.1 Flow of input and output files Each program is started with (at least) one command line argument, e.g. programx programx.def in which the arguments specifies a filename, in which FORTRAN I/O units are connected to unix filenames. (See examples at specific programs). These def -files are generated automatically when the standard WIEN2k scripts x, init lapw or run lapw are used, but may be tailored by hand for special applications. Using the option x program -d a def-file can be created without running the program. In addition each program reads/writes the following files: case.struct a master input file, which is described below (Section 4.3) case.inx a specific input file, where X labels the program (see def-files for each program in chapter 6). case.outputx an output file The programs of the SCF cycle (see figure 4.1) write the following files: case.scfx a file containing only the most significant output (see description below). program.error error report file, should be empty after successful completion of a program (see chapter 6) 33

52 34 CHAPTER 4. FILES AND PROGRAM FLOW Figure 4.1: Data flow during a SCF cycle (programx.def, case.struct, case.inx, case.outputx and optional files are omitted)

53 4.1. FLOW OF INPUT AND OUTPUT FILES 35 The following tables describe input and output files for the initialization programs nn, sgroup, symmetry, lstart, kgen, dstart (table 4.1), the utility programs tetra, irrep, spaghetti, aim, lapw7, elnes, lapw3, lapw5, xspec, optic, joint, kram, optimize and mini (table 4.2) as well as for a SCF cycle of a non-spin-polarized case (table 4.2). Optional input and output files are used only if present in the respective case subdirectory or requested/generated by an input switch. The connection between FORTRAN units and filenames are defined in the respective programx.def files. The data flow is illustrated in Fig program needs generates necessary optional necessary optional NN nn.def case.outputnn case.struct nn case.struct SGROUP case.struct case.outputsgroup case.struct sgroup SYMMETRY symmetry.def case.outputs case.struct st case.struct case.in2 st case.in2 st LSTART lstart.def case.outputst case.rspup case.struct case.rsp case.rspdn case.inst case.in0 st case.vsp st case.in1 st case.vspdn st case.in2 st case.sigma case.inc st case.inm st case.inm restart KGEN kgen.def case.outputkgen case.struct case.klist case.kgen DSTART dstart.def case.outputd case.struct case.clmsum(up) case.rsp(up) dstart.error case.in0 case.in0 std case.in1 case.in2 Table 4.1: Input and output files of init programs program needs generates necessary optional necessary optional SPAGHETTI spaghetti.def case.qtl case.spaghetti ps case.spaghetti ene case.insp case.outputso case.outputsp case.struct case.irrep case.band.agr case.output1 TETRA tetra.def case.outputt case.int case.qtl case.dos1(2,3) case.kgen case.energy case.dos1ev(1,2,3) case.scf2 LAPW3 lapw3.def case.output3 case.struct case.rho case.in2 case.clmsum case.clmsum LAPW5 lapw5.def case.sigma case.output5 case.rho.oned case.struct case.rho case.in5 case.clmval XSPEC xspec.def case.outputx case.coredens case.inc case.dos1ev case.int case.xspec case.vsp case.txspec case.struct case.m1 case.qtl case.m2 OPTIC optic.def case.outputop case.symmat1 case.struct case.symmat case.symmat2 case.mat diag case.inop case.vsp case.vector JOINT joint.def case.outputjoint case.sigma intra case.injoint case.joint case.intra continued on next page

54 36 CHAPTER 4. FILES AND PROGRAM FLOW case.struct case.kgen case.weight case.symmat case.mat diag KRAM kram.def case.epsilon case.eloss case.inkram case.sigmak case.sumrules case.joint OPTIMIZE case.struct case initial.struct optimize.job case vol xxxxx.struct case c/a xxxxx.struct MINI mini.def case.scf mini case.outputm case.clmsum inter case.inm case.tmpm case.tmpm1 case.finm case.constraint case.struct1 case.scf case.clmhist case.scf mini1 case.struct.min hess.minrestart IRREP case.struct case.outputirrep case.vector case.irrep AIM case.struct case.outputaim case.crit case.clmsum case.surf case.inaim LAPW7 case.struct case.output7 case.abc case.vector case.grid case.in7 case.psink case.vsp QTL case.struct case.outputq case.vector case.qtl case.inq case.vsp Table 4.2: Input and output files of utility programs program needs generates necessary optional necessary optional LAPW0 lapw0.def case.clmup/dn case.output0 case.r2v case.struct case.vrespsum/up/dn case.scf0 case.vcoul case.in0 case.inm case.vsp(up/dn) case.vtotal case.clmsum case.vns(up/dn) ORB orb.def case.energy case.outputorb case.br1orb case.struct case.vorb old case.scforb case.br2orb case.inorb case.vorb case.dmat orb.error case.vsp LAPW1 lapw1.def case.vns case.output1 case.nsh(s) case.struct case.vorb case.scf1 case.nmat only case.in1 case.vector.old case.vector case.vsp case.energy case.klist LAPWSO lapwso.def case.vorb case.vectorso case.struct case.outputso case.inso case.scfso case.in1 case.energyso case.vector case.normso case.vsp case.vns case.energy LAPW2 lapw2.def case.kgen case.output2 case.qtl case.struct case.nsh case.scf2 case.weight case.in2 case.weight case.clmval case.weigh case.vector case.weigh case.help03* case.vsp case.recprlist case.vrespval case.energy case.almblm case.radwf case.dmat LAPWDM lapwdm.def case.inso case.outputdm case.struct case.scfdm case.indm case.dmat case.vector lapwdm.error case.vsp case.weigh case.energy continued on next page

55 4.2. INPUT/OUTPUT FILES 37 SUMPARA case.struct case.scf2p case.outputsum case.clmval case.clmval case.scf2 LCORE lcore.def case.vns case.outputc case.corewf case.struct case.scfc case.inc case.clmcor case.vsp lcore.error After LCORE the case.scfx files are appended to case.scf and the case.clmsum file is renamed to case.clmsum old (see run lapw) MIXER mixer.def case.clmsum old case.outputm case.broyd* case.struct case.clmsc case.scfm case.inm case.clmcor case.clmsum case.clmval case.scf mixer.error case.broyd1 case.broyd2 case.dmat After MIXER the file case.scfm is appended to case.scf, so that after an iteration is completed, the two essential files are case.clmsum and case.scf. Table 4.3: Input and output files of main programs in an SCF cycle 4.2 Description of general input/output files In the following section the content of the (non-trivial) output files is described: case.almblm Contains the A lm, B lm, C lm coefficients of the wavefunctions (generated optional by lapw2). case.band.agr A xmgrace file with the energy bandstructure plot generated by spaghetti. case.broydx Contains the charge density of previous iterations if you use Broyden s method for mixing. They are removed when using save lapw. They should be removed by hand when calculational parameters (RKMAX, kmesh,... ) have been changed, or the calculation crashed due to a too large mixing and are restarted by using a new density generated by dstart. case.clmcor Contains the core charge density (as σ(r) = 4πr 2 ρ(r) and has only a spherical part). In spin-polarized calculations two files case.clmcorup and case.clmcordn are used instead. case.clmsc Contains the semi-core charge density in a 2-window calculation, which is no longer recommended. In spin-polarized calculations two files are used instead: case.clmscup and case.clmscdn. case.clmsum Contains the total charge density in the lattice harmonics representation and as Fourier coefficients. (The LM=0,0 term is given as σ(r) = 4πr 2 ρ(r), the others as r 2 ρ LM (r); suitable for generating electron density plots using lapw5 when the TOT-switch is set, (see section 8.13). In spin-polarized calculations two additional files case.clmup and case.clmdn contain the spin densities. Generated by dstart or mixer. case.clmval Contains the valence charge density as r 2 ρ LM (r); suitable for generating valence electron density plots using lapw5 when the VAL-switch is set, (see 8.13). In spin-polarized calculations two files case.clmvalup and case.clmvaldn are used instead. case.dmatup/dn Contains the density matrix generated by lapw2or lapwdm for LDA+U, OP or onsite-hybrid-dft calculations. case.dosx Contains the density of states (states/ry) and corresponding energy (in Ry at the internal energy scale) generated by tetra. X can be 1-3. Additional files case.dosxev contain the DOS in (states/ev) and the energy in ev with respect to EF. case.help03x Contains eigenvalues and partial charges for atom number X. case.kgen This file contains the indices of the tetrahedra in terms of the list of k-points. It is used in lapw2 (if EFMOD switch in case.in2 is set to TETRA, see 7.7.3) and in tetra. case.klist This file contains a list of k-points in the BZ on a (special k-point) tetrahedral mesh. It is generated in kgen. case.qtl Contains eigenvalues and corresponding partial charges (bandwise) in a form suitable for tetra and band structure plots with band character. The decomposition of these charges is controlled by ISPLIT in case.struct.

56 38 CHAPTER 4. FILES AND PROGRAM FLOW case.radwf Contains the radial basis functions inside spheres (generated optional by lapw2). case.rho Contains the electron densities on a grid in a specified plane generated by lapw5. This file can be used as input for your favorite contour or 3D plotting program. case.rsp Contains the atomic densities generated by lstart. They are used by dstart to generate a first crystalline density (case.clmsum). case.r2v Contains the exchange potential (in the lattice harmonics representation as r 2 V LM (r) and as Fourier coefficients) in a form suitable for plotting with lapw5. case.scf mini Contains the last scf-iteration of each individual time (geometry) step during a structural minimization using mini. Thus this file contains a complete history of properties (energy, forces, positions) during a structural minimization. case.sigma Contains the atomic densities for those states with a P in case.inst. Generated in lstart and used for difference densities in lapw5. case.spaghetti ps A ps file with the energy bandstructure plot generated by spaghetti. case.symmat Contains the momentum matrix elements between bands i,j. Created by optic and used in joint. case.vcoul Contains the Coulomb potential (in the lattice harmonics representation as r 2 V LM (r) and as Fourier coefficients) in a form suitable for plotting with lapw5. case.vorb Contains the orbital potential (in Ry) generated by orb for LDA+U or onsite-hybrid- DFT calculations in form of a (2l+1,2l+1) matrix. case.vtotal Contains the total potential (in the lattice harmonics representation as r 2 V LM (r) and as Fourier coefficients) in a form suitable for plotting with lapw5. case.vector Binary file, contains the eigenvalues and eigenvectors of all k-points calculated in lapw1. In spin-polarized calculations two files case.vectorup and case.vectordn are used instead. lapwso generates case.vectorso. case.energy Contains the eigenvalues of all k-points calculated in lapw1. In spin-polarized calculations two files case.vectorup and case.vectordn are used instead. lapwso generates case.energyso. case.vns Contains the non-spherical part of the total potential V. Inside the sphere the radial coefficients of the lattice harmonics representation are listed (for L greater than 0), while for the interstitial region the reanalyzed Fourier coefficients are given (see equ. (2.10)). In spinpolarized calculations two files case.vnsup and case.vnsdn are used instead. case.vorbup/dn Contains the orbital dependent part of the potential in LDA+U, OP or Hybrid- DFT calculations. Generated in orb, used in lapw1. case.vsp Contains the spherical part of the total potential V stored as r V (thus the first values should be close to 2 Z). In spin-polarized calculations two files case.vspup and case.vspdn are used instead. 4.3 The master input file case.struct The file case.struct defines the structure and is the main input file used in all programs. We provide several examples in the subdirectory example struct file If you are using the Struct Generator from the graphical user interface w2web, or the makestruct lapw utility, you don t have to bother with this file directly, but generate it by specifying the relevant data in a mask. Alternatively, the utilities cif2struct or xyz2struct convert the corresponding cif or xyz files to the WIEN2k-format. However, the description of the fields of this master input file can be found here. Note: If you are changing this file manually, please note that this is a formatted file and the proper column positions of the characters are important! Use REPLACE instead of DELETE and INSERT during edit! Also some parameters are usually element-specifically chosen (R0)

57 4.3. THE CASE.STRUCT.FILE 39 We start the description of this file with an abridged example for rutile TiO 2 (adding line numbers): top of file line # Titaniumdioxide TiO2 (rutile): u= P LATTICE,NONEQUIV. ATOMS 2 2 MODE OF CALC=RELA ATOM -1: X= Y= Z= MULT= 2 ISPLIT= 8 6 ATOM -1: X= Y= Z= Titanium NPT= 781 R0= RMT= Z: LOCAL ROT MATRIX: ATOM -2: X= Y= Z= MULT= 4 ISPLIT= 8 ATOM -2: X= Y= Z= ATOM -2: X= Y= Z= ATOM -2: X= Y= Z= Oxygen NPT= 781 R0= RMT= Z: 8.0 LOCAL ROT MATRIX: SYMMETRY OPERATIONS: bottom of file Interpretive comments on this file are as follows. P all primitive lattices except hexagonal [a sin(γ ) sin(β), a cos(γ ) sin(β), (a cos(β))], [0, b sin(α), b cos(α)], [0, 0, c] F face-centered [a/2, b/2, 0], [a/2, 0, c/2], [0, b/2, c/2] B body-centered [a/2, -b/2, c/2],[a/2, b/2, -c/2], [-a/2, b/2, c/2] CXY C-base-centered (orthorhombic only) [a/2, -b/2, 0], [a/2, b/2, 0], [0, 0, c] CYZ A-base-centered (orthorhombic only) [a, 0, 0], [0, -b/2, c/2], [0, b/2, c/2] CXZ B-base-centered (orthorh. and monoclinic [a sin(γ)/2, a cos(γ)/2, -c/2], [0, b, 0], [a sin(γ)/2, a symmetry) cos(γ)/2, c/2] R rhombohedral [a/ 3/2, -a/2, c/3],[a/ 3/2, a/2, c/3],[-a/ 3, 0, c/3] H hexagonal [ 3a/2, -a/2, 0],[0, a, 0],[0, 0, c] Table 4.4: Lattice type, description and bravais matrix used in WIEN2k. The angle γ is defined via cos(γ) = cos(γ ) sin(α) sin(β) + cos(β) cos(α) line 1: format (A80) title (compound) line 2: format (A4,23X,I3) lattice type, NAT lattice type NAT as defined in table 4.4. For centered monoclinic lattices only the CXZ setting is supported and the monoclinic angle must be gamma. Eventually you have to transform a given spacegroup setting into one supported in WIEN2k (for instance for SG #12 we need (B112/m) or (B2/m11) setting and not (C122/m1) or (C2/m11) (it depends on your starting setting, but the final setting must have a monoclinic angle gamma); for SG #15 we need (B2/b) or one of the alternative B settings, but not one of the many others) using the Bilbao crystallographic server (http://www.cryst.ehu.es/; structure utilities ; SETSTRU) number of inequivalent atoms in the unit cell

58 40 CHAPTER 4. FILES AND PROGRAM FLOW line 3: format (13X,A4) mode RELA NREL fully relativistic core and scalar relativistic valence non-relativistic calculation line 4: format (6F10.6) a, b, c, α, β, γ a, b, c unit cell parameters (in a.u., 1 a.u. = Å). In face- or body-centered structures the non-primitive (cubic) lattice constant, for rhombohedral (R) lattices the hexagonal lattice constants must be specified. (The following may help you to convert between hexagonal and rhombohedral specifications: a hex = 2cos( π α rhomb )a 2 rhomb c hex = 3 a 2 rhomb 1 3 a2 hex and (for fcc-like lattices) a rhomb = a cubic / 2 α, β, γ angles between unit axis (if omitted, 90 is set as default). Set it only for P and CXZ lattices line 5: format (4X,I4,4X,F10.8,3X,F10.8,3X,F10.8) atom-index, x, y, z atomindex x,y,z running index for inequivalent atoms positive in case of cubic symmetry negative for non-cubic symmetry this is set automatically using symmetry position of atom in internal units, i.e. as positive fractions of unit cell parameters. (0 x 1; the positions in the unit cell are consistent with the convention used in the International Tables of Crystallography 64. In face- (body-) centered structures only one of four (two) atoms must be given, eg. in Fm3m position 8c is specified with 0.25, 0.25, 0.25 and.75, 0.75, 0.75). For R lattice use rhombohedral coordinates. (To convert from hexagonal into rhombohedral coordinates use the auxiliary program hex2rhomb, which can be called at a command-line: X ortho = X hex X rhomb = X ortho line 6: format (15X,I2,17X,I2) multiplicity, isplit multiplicity number of equivalent atoms of this kind isplit this is just an output-option and is used to specify the decomposition of the lm-like charges into irreducible representations, useful for interpretation in case.qtl). This parameter is automatically set by symmetry: 0 no split of l-like charge 1 p-z, (p-x, p-y) e.g.:hcp 2 e-g, t-2g of d-electrons e.g.:cubic 3 d-z2, (d-xy,d-x2y2), (d-xz,dyz) e.g.:hcp 4 combining option 1 and 3 e.g.:hcp 5 all d symmetries separate 6 all p symmetries separate 8 combining option 5 and 6-2 d-z2, d-x2y2, d-xy, (d-xz,d-yz)

59 4.3. THE CASE.STRUCT.FILE split lm like charges (for old telnes, not necessary anymore) 99 calculate cross-terms (for old telnes, not necessary anymore) >>>: line 5 must now be repeated MULT-1 times for the other positions of each equivalent atom according to the Wyckoff position in the International Tables of Crystallography. line 7: format (A10,5X,I5,5X,F10.8,5X,F10.5,5X,F5.2) name of atom, NPT, R0, RMT, Z name of atom NPT R0 RMT Z Use the chemical symbol. Positions 3-10 for further labeling of nonequivalent atoms (use a number in position 3) number of radial mesh points (381 gives a good mesh for LDA calculations, but for GGA twice as many points are recommended; always use an odd number of mesh points!) the radial mesh is given on a logarithmic scale: r(n) = R 0 e [(n 1) DX] first radial mesh point (typically between and , smaller for heavy elements, bigger for light ones; a struct-file generated by w2web will have proper R0 values.) atomic sphere radius (muffin-tin radius), can easily be estimated after running nn (see 6.1) and are set automatically with setrmt lapw see 5.2.7). The following guidelines will be given here: Choose spheres as large as possible as this will save MUCH computer time. But: Use identical radii within a series of calculations (i.e. when you want to compare total energies) therefore consider first how close the atoms may possibly come later on (volume or geometry optimization); do NOT make the spheres too different (even when the geometry would permit it), instead use the largest spheres for f-electron atoms, % smaller ones for d-elements and again % smaller for sp-elements; H is a special case, you may choose it much smaller (e.g. 0.6 and 1.2 for H and C) and systems containing H need a much smaller RKMAX value (3-5) in case.in1. atomic number line 8-10: format (20X,3F10.7) ROTLOC local rotation matrix (always in an orthogonal coordinate system). Transforms the global coordinate system (of the unit cell) into the local at the given atomic site as required by point group symmetry (see in the INPUT-Section of LAPW2). SYMMETRY calculates the point group symmetry and determines ROTLOC automatically. Note, that a proper ROTLOC is required, if the LM values generated by SYMMETRY are used. A more detailed description with several examples is given in the appendix A and sec >>>: lines 5 thru 10 must be repeated for each inequivalent atom line 11: format (I4) nsym number of symmetry operations of space group (see International Tables of Crystallography 64) If nsym is set to zero, the symmetry operations will be generated automatically by SYMMETRY. line 12-14: format (3I2,F10.7) matrix, tau (as listed in the International Tables of Crystallography 64) matrix tau matrix representation of (space group) symmetry operation non-primitive translation vector line 15: format (I8) index of symmetry operation specified above >>>: lines 12 thru 15 must be repeated for all other symmetry operations

60 42 CHAPTER 4. FILES AND PROGRAM FLOW line 16: free format (optional) after a line Precise positions, a list of all atomic positions can follow with full machine precision. These coordinates are written by mixer if one performs a MSR1a structure optimization and they will be used instead of the truncated numbers read above (only if they agree, but not if one modifies them by hand such that they differ more significantly. 4.4 The history file case.scf During the self-consistent field (SCF) cycle the essential data are appended to the file case.scf in order to generate a summary of previous iterations. For an easier retrieval of certain quantities the essential lines are labeled with :LABEL:, which can be used to monitor these quantities during self-consistency as explained below. The most important :LABELs are :ENE :WAR :DIS :FER :GAP :FORxx :FGLxx :FR :DTOxx :CTOxx :NTOxx :QTLxx :EPLxx :EPHxx :EFGxx :ETAxx :RTOxx :VZERO total energy (Ry). If there is a WARNING mentioned, check :WAR contains some warnings indicating that there might be a problem with your calculations. Usually these problems are not fatal, but may influence the accuracy. charge distance between last 2 iterations ( ρ n ρ n 1 dr). Good convergence criterium. Fermi energy (and Fermi-method) energy gap (for insulators). Please note, this value will only be correct, if the VBM/CBM are in your k-mesh. ( Shifted k-meshes do not contain tha Gamma-point and often gaps are at Gamma!!) force on atom xx in mry/bohr (in the local (for each atom) cartesian coordinate system) force on atom xx in mry/bohr (in the global coordinate system of the unit cell (in the same way as the atomic positions are specified)) in MSR1a mode prints information about the remaining size of the forces and whether it will/has switched to MSR1 mode. total difference charge density for atom xx between last 2 iterations total charge in sphere xx (mixed after MIXER) total charge in sphere xx (new (not mixed) from LAPW2+LCORE) partial charges in sphere xx l-like partial charges and mean energies in lower (semicore) energy window for atom xx. Used as energy parameters in case.in1 for next iteration l-like partial charges and mean energies in higher (valence) energy window for atom xx. Used as energy parameters in case.in1 for next iteration Electric field gradient (EFG) V zz for atom xx Asymmetry parameter of EFG for atom xx Density for atom xx at the nucleus (first radial mesh point) Gives the total, Coulomb and xc-potential at z=0 and z=0.5 (meaningfull only for slab calculations) To check to which type of calculation a scf file corresponds use: :POT :LAT :VOL :POSxx :RKM :NEC Exchange-correlation potential used in this calculation Lattice parameters in this calculation Volume of the unit cell Atomic positions for atom xx (as in case.struct) Actual matrix size and resulting RKmax normalization check of electronic charge densities. If a significant amount of electrons is missing, one might have core states, whose charge density is not completely confined within the respective atomic sphere. In such a case the corresponding states should be treated as band states (using LOs). For spin-polarized calculations: :MMTOT Total spin magnetic moment/cell

61 4.5. FLOW OF PROGRAMS 43 :MMIxx :CUPxx :CDNxx :NUPxx :NDNxx :ORBxx :HFFxx Spin magnetic moment of atom xx. Note, that this value depends on RMT. spin-up charge (mixed) in sphere xx spin-dn charge (mixed) in sphere xx spin-up charge (new, from lapw2+lcore) in sphere xx spin-dn charge (new, from lapw2+lcore) in sphere xx Orbital magnetic moment of atom xx (needs SO calculations and LAPWDM). Hyperfine field of atom xx (in kgauss). One can monitor the energy eigenvalues (listed for the first k-point only), the Fermi-energy or the total energy. Often the electronic charges per atom reflect the convergence. Charge transfer between the various atomic spheres is a typical process during the SCF cycles: large oscillations should be avoided by using a smaller mixing parameter; monotonic changes in one direction suggest a larger mixing parameter. In spin-polarized calculations the magnetic moment per atomic site is an additional crucial quantity which could be used as convergence criterion. If a system has electric field gradients and one is interested in that quantity, one should monitor the EFGs, because these are very sensitive quantities. It is best to monitor several quantities, because often one quantity is converged, while another still changes from iteration to iteration. The script run lapw has three different convergence criteria built in, namely the total energy, the atomic forces and the charge distance (see 5.1.3, 5.1.4). We recommend the use of UNIX commands like : grep :ENE case.scf or use Analysis from w2web for monitoring such quantities. You may define an alias for this (see sec. 11.2), and a csh-script grepline lapw is also available to get a quantity from several scf-files simultaneously (sec and 5.3). 4.5 Flow of programs The WIEN2k package consists of several independent programs which are linked via C-SHELL SCRIPTS described below. The flow and usage of the different programs is illustrated in the following diagram (Fig. 4.2): The initialization consists of running a series of small auxiliary programs, which generates the inputs for the main programs. One starts in the respective case/ subdirectory and defines the structure in case.struct (see 4.3). The initialization can be invoked by the script init lapw (see sec. 3.7 and 5.1.3), and consists of running: SETRMT a perl-program which helps to select proper RMT values NN a program which lists the nearest neighbor distances up to a specified limit (defined by a distance factor f) and thus helps to determine the atomic sphere radii. In addition it is a very useful additional check of your case.struct file (equivalency of atoms) SGROUP determines the spacegroup of the structure defined in your case.struct file. SYMMETRY generates from a raw case.struct file the space group symmetry operations, determines the point group of the individual atomic sites, generates the LM expansion for the lattice harmonics and determines the local rotation matrices. LSTART generates free atomic densities and determines how the different orbitals are treated in the band structure calculations (i.e. as core or band states, with or without local orbitals,... ). KGEN generates a k-mesh in the irreducible part of the BZ. DSTART generates a starting density for the scf cycle by a superposition of atomic densities generated in LSTART.

62 44 CHAPTER 4. FILES AND PROGRAM FLOW NN check for overlap. spheres SGROUP struct files SYMMETRY struct files input files LSTART atomic calculation Hψ nl = E nl ψ nl atomic densities input files KGEN DSTART superposition of atomic densities ρ k mesh generation ORB LDA+U, OP potentials LAPW0 2 V C = 8πρ Poisson V XC ( ρ) LDA V= V C + V XC V LAPW1 2 + V ψ k = E k ψ k V MT LCORE atomic calculation Hψ nl = E nl ψ nl E k ψ k LAPWSO ρ core E core add spin orbit interaction LAPW2 ρ val = Σ ψ k ψ k E k < EF ρ val ρ old LAPWDM calculates density matrix MIXER ρ new = ρold ( ρ val + ρ core ) ρ new STOP yes converged? no Figure 4.2: Program flow in WIEN2k

63 4.5. FLOW OF PROGRAMS 45 Then a self-consistency cycle is initiated and repeated until convergence criteria are met (see 3.8 and 5.1.4). This cycle can be invoked with a script run lapw, and consists of the following steps: LAPW0 (POTENTIAL) generates potential from density LAPW1 (BANDS) calculates valence bands (eigenvalues and eigenvectors) LAPW2 (RHO) computes valence densities from eigenvectors LCORE computes core states and densities MIXER mixes input and output densities Core, semi-core and valence states In many cases it is desirable to distinguish three types of electronic states, namely core, semi-core and valence states. For example titanium has core (1s, 2s, 2p), semi-core (3s, 3p) and valence (3d, 4s, 4p) states. In our definition core states are only those whose charge is entirely confined inside the corresponding atomic sphere. They are deep in energy, e.g., more than 7-10 Ry below the Fermi energy. Semi-core states lie high enough in energy (between about 1 and 7 Ry below the Fermi energy), so that their charge is no longer completely confined inside the atomic sphere, but has a few percent outside the sphere. Valence states are energetically the highest (occupied) states and always have a significant amount of charge outside the spheres. The energy cut-off specified in lstart during init lapw (usually -6.0 Ry) defines the separation into core- and band-states (the latter contain both, semicore and valence). If a system has atoms with semi-core states, then the best way to treat them is with local orbitals, an extension of the usual LAPW basis. An input for such a basis set will be generated automatically. (Additional LOs can also be used for valence states which have a strong variation of their radial wavefunctions with energy (e.g. d states in TM compounds) to improve the quality of the basis set, i.e. to go beyond the simple linearization) Spin-polarized calculation For magnetic systems spin-polarized calculations can be performed. In such a case some steps are done for spin-up and spin-down electrons separately and the script runsp lapw consists of the following steps: LAPW0 (POTENTIAL) generates potential from density LAPW1 -up (BANDS) calculates valence bands for spin-up electrons LAPW1 -dn (BANDS) calculates valence bands for spin-down electrons LAPW2 -up (RHO) computes valence densities for spin-up electrons LAPW2 -dn (RHO) computes valence densities for spin-down electrons LCORE -up computes core states and densities for spin-up electrons LCORE -dn computes core states and densities for spin-down electrons MIXER mixes input and output densities The use of spin-polarized calculations is illustrated for fcc Ni (section 10.2), one of the test cases provided in the WIEN2k package Fixed-spin-moment (FSM) calculations Using the script runfsm lapw -m XX it is possible to constrain the total spin magnetic moment per unit cell to a fixed value XX and thus force a particular ferromagnetic solution (which may not correspond to the equillibrium). This is particularly useful for systems with several metastable

64 46 CHAPTER 4. FILES AND PROGRAM FLOW (non-) magnetic solutions, where conventional spin-polarized calculation would not converge or the solution may depend on the starting density. Additional SO-interaction is not supported. Please note, that once runfsm lapw has finished, only case.vectordn is ok, but case.vectorup is NOT the proper up-spin vector and MUST NOT be used for the calculations of QTLs (and DOS). It must be regenerated by x lapw1 -up (see also the comments for iterative diagonalization in section ) Antiferromagnetic (AFM) calculations Several considerations are necessary, when you want to perform an AFM calculation. Please have also a look into $WIENROOT/SRC afminput/afminput test. You must construct a unit cell which allows for the desired AF ordering. For example for bcc Cr you must select a P lattice and specify both atoms, Cr1 at (0,0,0) and Cr2 at (.5,.5,.5), corresponding to a CsCl structure. Note, that it is important to label the two Cr atoms with Cr1 and Cr2, since only then the symmetry programs can detect that those atoms should be different (although they have the same Z). If sgroup has interchanged some axis, try to undo these changes, since afminput may not properly find the correct symmetry operations in such a case. When you generate case.inst you must specify the correct magnetic order and flip the spin of the AF atoms (i.e. invert the spin up and dn occupation numbers). In addition you should set a zero moment (identical spin up and dn occupations) for all non-magnetic atoms. This can be done conveniently using instgen lapw -ask or during initialization using w2web. Now you can run either a normal spinpolarized initialization (without AFM option) and runsp lapw or: Create a struct file of the non-magnetic (or ferro-magnetic) supergroup (run init lapw up to lstart). Name it case.struct supergroup. (For example for bcc Cr, this would be a struct file with the ordinary cubic lattice parameters, B type lattice and just one Cr at (0,0,0).) Run init lapw. At the end AFMINPUT creates an input file for the program CLMCOPY. Depending on the presence of case.struct supergroup and the specific symmetry it may/may not ask you to supply a symmetry operation/nonprimitive translation (see Sect Run runafm lapw. This script calls LAPW1 and LAPW2 only for spin-up but the corresponding spin-dn density is created by CLMCOPY according to the rules defined during initialization. This reduces the required cpu time by a factor of 2 (and in addition the scf cycle is much more stable). It is highly recommended that you save your work (save lapw) and check the results by continuing with a regular runsp lapw. If nothing changes (E-tot and other properties), then you are ok, otherwise make sure the scf calculation is well converged (-cc or better). Eventually the system may not want to be antiferromagnetic (but for instance it is ferrimagnetic!). runafm lapw saves you more than a factor of 2 in in computer time, since only spin-up is calculated and in addition the scf-convergence may be MUCH faster. It works also with LDA+U (case.dmatup/dn are also copied), but does NOT work with Hybrid-DFT nor spin-orbit coupling, since this requires the presence of both vector files in the LAPWSO step Spin-orbit interaction You can add spin-orbit interaction in LAPWSO (called directly after LAPW1) using a secondvariational method with the scalar-relativistic orbitals (from LAPW1) as basis. The number of

65 4.5. FLOW OF PROGRAMS 47 eigenvalues will double since SO couples spin-up and dn states, so they are no longer separable. In addition, LOs with a p 1/2 radial basis can be added. (Kunes et al. 2001) To assist with the generation of the necessary input files and possible changes in symmetry, a script initso lapw exists. For non-spinpolarized cases nothing particular must be taken into account and SO can be easily applied by running run lapw -so. It will automatically use the complex version of LAPW2. However, for spin-polarized cases, the SO interaction may change (lower) the symmetry depending on how you choose the direction of magnetization and care must be taken to get a proper setup. initso lapw together with symmetso generates the proper symmetry. Just a few hints what can happen: Suppose you have a cubic system and put the magnetization along [001]. This will create a tetragonal symmetry (and you can temporarely tell this to the initialization programs by changing the respective lattice parameter c to a tetragonal system). If you put the magnetization along [111], this creates most likely a rhombohedral (or hexagonal) symmetry. (Try to visualize this for a fcc lattice, XCRYSDEN is very useful for this purpose). Symmetry operations can be classified into operations which invert the magnetization,others which leave it unchanged and some which do some arbitrary rotation. The program symmetso (part of initso lapw) sorts these operations in the proper way. If you don t have inversion symmetry in the original structure, you must not add inversion in KGEN. The recommended way to include SO in the calculations is to run a regular scf calculation first, save the results, initialize SO and run another scf cycle including SO: run[sp] lapw save lapw case nrel initso lapw run[sp] lapw -so For spin-polarized systems you may want to add the -dm switch to calculate also the orbital magnetic moment Orbital potentials In WIEN2kit is possible to go beyond standard LDA (GGA) and include orbital dependent potentials in methods like LDA+U or the Orbital-Polarization, which are very useful for strongly correlated systems. To use these features you need to create input-files for LAPWDM and ORB (case.indm, case.inorb). You may copy a template from SRC templates, but must modify it according to your needs. In particular you must select for which atoms and which orbitals (usually d-orbitals of late transition metal atoms or f-orbitals for 4f/5f atoms) you want to add such a potential and also choose the proper U and J values for them. Once this is done, you can include this using the -orb switch. The density matrix (case.dmatup/dn) will be calculated in lapw2 (or in lapwdm when spin-orbit is also used), it will be mixed in mixer (consistently with the regular charge density) and the orbital dependent potentials will be calculated on orb (after lapw0). Note, you must run spin-polarized in order to use orbital potentials. runsp lapw -orb [-so]

66 48 CHAPTER 4. FILES AND PROGRAM FLOW If you want to force a non-magnetic solution you can constrain the spin-polarization to zero using runsp c lapw. Without SO, case.vorbup/dn will be considered in LAPW1(c). With SO, it will be applied in LAPWSO (and allows coupling of nondiagonal spin-terms) Onsite-exact-exchange and hybrid functionals for correlated electrons In WIEN2k, it is also possible to go beyond standard LDA (GGA) and include onsite-exactexchange (i.e., Hartree-Fock), which is very useful for strongly correlated systems, since such calculations are computationally nearly as cheap as standard DFT (or LDA+U). The onsite-exactexchange/hybrid methods apply HF only inside the atomic spheres and only to one particular orbital. Thus you can use it only for localized electrons (see Tran et al for details). Onsiteexact-exchange will NOT improve gaps in sp-semiconductors. For these systems you have to use full hybrid-dft (see Sec.4.5.8) or the mbj potential (see Sec.4.5.9) The one-parameter onsite hybrid functionals have the general following form: Exc onsite hybrid [ρ] = Exc SL [ρ] + α ( Ex HF [Ψ corr ] Ex SL [ρ corr ] ) where Exc SL is the underlying semilocal (SL) functional. The following semilocal functionals can be used in E onsite hybrid xc : LDA: XC LDA (indxc=5) in case.in0. mode=hybr and fraction=α in case.ineece PBE: XC PBE (indxc=13) in case.in0. mode=hybr and fraction=α in case.ineece WC: XC WC (indxc=11) in case.in0. mode=hybr and fraction=α in case.ineece PBEsol: XC PBESOL (indxc=19) in case.in0. mode=hybr and fraction=α in case.ineece TPSS: XC TPSS (indxc=27) in case.in0. mode=hybr and fraction=α in case.ineece The three-parameter onsite hybrid functionals B3PW91 and B3LYP are also available. These two functionals were proposed with the fraction of exact exchange α = 0.2, however other values for α can be chosen as well. B3PW91: EX B3PW91 EC B3PW91 VX B3PW91 VC B3PW91 (indxc=18) in case.in0. mode = HYBR and fraction = 0.2 in case.ineece. E onsite B3PW91 xc [ρ] = Exc LDA [ρ] ( Ex HF [Ψ corr ] Ex LDA [ρ corr ] ) ( Ex B88 [ρ] Ex LDA [ρ] ) ( Ec PW91 [ρ] Ec LDA [ρ] ) where Ec LDA = Ec PW92. B3LYP: XC B3LYP (indxc=47) in case.in0. case.ineece. E onsite B3LYP where E LDA c xc [ρ] = Exc LDA = E VWN5 c. Onsite Hartree-Fock calculations, i.e., mode = HYBR and fraction = 0.2 in [ρ] ( Ex HF [Ψ corr ] Ex LDA [ρ corr ] ) ( Ex B88 [ρ] Ex LDA [ρ] ) ( Ec LYP [ρ] Ec LDA [ρ] ) Exc onsite HF [ρ] = E SL xc [ρ] + Ex HF are also possible with the following semilocal functionals. [Ψ corr ] E SL xc [ρ corr ]

67 4.5. FLOW OF PROGRAMS 49 LDA: XC LDA (indxc=5) in case.in0. mode=eece and fraction=1 in case.ineece PBE: XC PBE (indxc=13) in case.in0. mode=eece and fraction=1 in case.ineece WC: XC WC (indxc=11) in case.in0. mode=eece and fraction=1 in case.ineece PBEsol: XC PBESOL (indxc=19) in case.in0. mode=eece and fraction=1 in case.ineece TPSS: XC TPSS (indxc=27) in case.in0. mode=eece and fraction=1 in case.ineece In addition to the input files which are necessary for an usual LDA or GGA calculation, the input file case.ineece is necessary to start a calculation. You may copy a template from SRC templates, but must modify it according to your needs. In particular you must select for which atoms and which orbitals (usually d-orbitals of late transition metal atoms or f-orbitals for 4f/5f atoms) you want to add such a potential and which type of functional you want to use. A sample input for calculations with exact exchange is given below top of file: case.ineece emin, natorb st atom index, nlorb, lorb nd atom index, nlorb, lorb HYBR HYBR / EECE mode 0.25 fraction of exact exchange bottom of file Interpretive comments on this file are as follows: line 1: free format emin, natom emin natorb lower energy cutoff, to be selected so that the energy of correlated states is larger than emin number of atoms for which the exact exchange is calculated line 2: free format iatom(i), nlorb(i), (lorb(li,i), li=1,nlorb(i)) iatom nlorb lorb index of atom in struct file number of orbital moments for which exact exchange shall be calculated orbital numbers (repeated nlorb-times) 2 nd line repeated natorb-times line 3: free format mode HYBR EECE means that LDA/GGA exchange will be replaced by exact exchange means that LDA/GGA exchange-correlation will be replaced by exact exchange line 4: free format alpha This is the fraction of Hartree-Fock exchange (between 0 and 1) As with LDA+U, hybrid functionals can be used only for spin-polarized calculations (runsp lapw with the switch -eece). runsp lapw will internally call runeece lapw, which will create all necessary additional input files (it requires a case.in0 file including the optional IFFT line as generated by init lapw): case.indm (case.indmc), case.inorb, case.in0eece, case.in2eece (case.in2ceece) and once this is done, calculates in a series of lapw2/lapwdm/lapw0/orb calculations the corresponding orbital dependent potentials.

68 50 CHAPTER 4. FILES AND PROGRAM FLOW runsp lapw -eece [-so] Unscreened and screened hybrid functionals ( hf -module) The onsite exact-exchange/hybrid functionals from can be applied only to localized electrons (typically 3d or 4f), but lead to cheap calculations. In WIEN2k, it is also possible to apply hybrid (and Hartree-Fock) functionals to all electrons, however this leads to calculations which are one or two orders of magnitude more expensive. Hybrid functionals are usually more accurate than the semilocal functionals for the electronic properties of semiconductors and insulators. They also give accurate results for strongly correlated systems like NiO. In hybrid functionals a fraction α of semilocal (SL) exchange is replaced by Hartree-Fock (HF) exchange: ). E hybrid xc = Exc SL + α ( Ex HF E SL x Hybrid functionals can also be constructed by considering only the short-range part of Ex HF and, which leads to the so-called screened hybrid functionals. In WIEN2k, the unscreened and E SL x screened hybrid functionals are implemented using the second-variational procedure (Tran and Blaha 2011). A few important points should be noted: Both, k-point and MPI parallelizations can be used (simultaneously or only one of them). As usual, the k-point parallelization is over the k-points in the irreducible Brillouin zone. The MPI parallelization is implemented in two subroutines which calculate the Hamiltonian and HF exchange energy, the latter being used only if option -nonself is set (see below). In the subroutine for the Hamiltonian, two separate loops are parallelized with MPI. The first loop is over the number of occupied bands and the second is over the total number of atoms in the unit cell ( NAT*MULT ). Note, however, that when option -diaghf is set (see below), the second loop is not executed. The same is done inside the subroutine for the HF exchange energy, the only difference being that the second loop is over the inequivalent atoms only ( NAT ). This has to be kept in mind, when you specify the number of MPI-jobs (it does not make sense for a cell with 2 atoms to MPI-parallelize with 64 cores). Due to the orbital-dependency of the HF potential, the files case.vectorhf, case.energyhf and case.weighhf are also saved when save lapw is executed. If you restart a calculation without case.vectorhf, then, for the first iteration, it will be generated from the semilocal potential (lapw1), and therefore the number of scf iterations to reach convergence will be larger. It is not possible to use spin-orbit coupling (-so) with hybrid functionals. case.vectorhf contains the orbitals for all k-points in the full Brillouin zone (while for case.vector it is only in the irreducible Brillouin zone). The available functionals Among the semilocal functionals Exc SL available in WIEN2k, only a few of them can be used in Exc hybrid (both in unscreened and screened modes). The functionals are the following (case.in0 grr is for the exchange part Ex SL ): LDA: XC LDA (indxc=5) in case.in0 and EX SLDA VX SLDA (indxc=51) in case.in0 grr PBE: XC PBE (indxc=13) in case.in0 and EX SPBE VX SPBE (indxc=52) in case.in0 grr. The functionals PBE0 and YS-PBE0 (similar to HSE06) correspond to α = 0.25 in case.inhf (see 7.4). WC: XC WC (indxc=11) in case.in0 and EX SWC VX SWC (indxc=53) in case.in0 grr PBEsol: XC PBESOL (indxc=19) in case.in0 and EX SPBESOL VX SPBESOL (indxc=54) in case.in0 grr

69 4.5. FLOW OF PROGRAMS 51 BPW91: EX B88 VX B88 EC PW91 VC PW91 (indxc=17) in case.in0 and EX SB88 VX SB88 (indxc=55) in case.in0 grr. (this is not B3PW91). BLYP: EX B88 VX B88 EC LYP VC LYP (indxc=24) in case.in0 and EX SB88 VX SB88 (indxc=55) in case.in0 grr. (this is not B3LYP). In addition, calculations with the well-known B3PW91 and B3LYP (with VWN5) unscreened hybrid functionals (see for the functionals form) can also be done: B3PW91: XC B3PW91 (indxc=18) in case.in0, EX SLDA VX SLDA (indxc=51) in case.in0 grr and α = 0.2 in case.inhf B3LYP: XC B3LYP (indxc=47) in case.in0, EX SLDA VX SLDA (indxc=51) in case.in0 grr and α = 0.2 in case.inhf Hartree-Fock calculations (without correlation) are also possible: HF: EX LDA VX LDA (indxc=6) in case.in0, EX SLDA VX SLDA (indxc=51) in case.in0 grr and α = 1 in case.inhf Flow in run lapw -hf The flow of programs during a scf iteration when executing run lapw -hf is the following (nonspin-polarized and real case): x lapw0 -grr (semilocal exchange) x lapw0 (semilocal exchange-correlation) x lapw1 (semilocal orbitals) x lapw2 (semilocal bands) mv case.vectorhf case.vectorhf old x hf (hybrid orbitals) cp case.klist fbz case.klist, cp case.kgen fbz case.kgen x lapw2 -hf (hybrid electron density and bands) cp case.klist ibz case.klist, cp case.kgen ibz case.kgen x lcore x mixer Self-consistent calculation The steps to perform a calculation with hybrid functionals are the following: Do a calculation with the underlying semilocal functional Exc SL mandatory). save the semilocal calculation. (recommended but not The next steps can be done conveniently using init hf lapw [-up]: create case.inhf (cp $WIENROOT/SRC templates/template.inhf case.inhf). While there are (more or less) reasonable default values for most parameters, you must set nband manually. Set nband to at least the number of occupied bands plus one. Larger values are more accurate, but be aware that computing time scales as nband 2. The value of nband which leads to a converged result will strongly depend on the studied system and property (e.g., much higher for EFG than for band gap or lattice constant). create case.in0 grr (cp case.in0 case.in0 grr), this file contains:

70 52 CHAPTER 4. FILES AND PROGRAM FLOW a screened exhccange functional (EX SLDA,... or indxc=51, 52, 53, 54 or 55) for the exchange functional (see above) R2V option (instead of NR2V ) such that the exchange potential is written to case.r2v grr KXC (instead of TOT ) such that αex SL is printed in case.scf0 grr (and case.scf) under the label :AEXSL In case.inc the print switch has to be 1 for all atoms such that the core orbitals are printed in case.corewf (you don t have to set this manually, the script run lapw will do it automatically when -hf is specified). if nband is large, you may have to edit case.in1 and set EMAX to a higher value (e.g., 5 Ry). Execute run kgenhf lapw. This generates case.klist fbz, case.kgen fbz, case.klist ibz, case.kgen ibz and case.outputkgenhf. One must use identical k-meshes and shifts for IBZ and FBZ. Note that the k-parallelization is done over the k-points specified in case.klist ibz (irreducible Brillouin zone). All these steps above can be conveniently performed using the script init hf lapw. Once the initializations has been done, execute run lapw (or runsp lapw) with the switch -hf: run(sp) lapw -hf... Neglect of the nondiagonal terms If only the eigenvalues are wanted, you may use the switch -diaghf. By using this switch, only the diagonal elements of the 2nd variational Hamiltonian matrix are calculated (the non-diagonal elements are set to zero). This leads to a much faster calculation of the eigenvalues, while keeping a very good accuracy (Tran 2012). However, the orbitals will not be modified, therefore running the calculation for more than one iteration is useless (the result will not change except for metallic systems). This option is not recommended for systems which are described as metallic with the semilocal functional or for difficult systems (e.g., NiO, see Tran 2012). It is important to be aware that with this option, the total energy (:ENE in case.scf) is nonsense unless the option -nonself (see below) was also used. After having done and saved a well converged calculation with the semilocal functional, the setting up of such a calculation is the same as for a self-consistent calculation (see above), but then run(sp) lapw is executed with -diaghf (-hf and -i 1 will be set automatically): run(sp) lapw -diaghf... Using a reduced k-mesh for the HF potential In order to reduce the computational time for the calculation of the HF potential, the internal loop over the k-points can be reduced to a subset of k-points. For instance, for a calculation with a k-mesh, the reduced k-mesh for the HF potential can be one of the following: 6 6 6, 4 4 4, 3 3 3, or This option, which should be used only in the case of screened exchange (see Paier et al. 2006), is particularly interesting for total energy calculations. Obviously, choosing such a reduced k-mesh is an approximation which needs to be tested. The setting up of such a calculation is the same as for a self-consistent calculation (see above), but with the switch -redklist when executing run kgenhf lapw (to create also case.klist rfbz): and run(sp) lapw: run kgenhf lapw -redklist run(sp) lapw -hf -redklist...

71 4.5. FLOW OF PROGRAMS 53 Non-self-consistent calculation of the total energy for hybrid functionals It is possible to calculate the total energy non-self-consistently, i.e., by plugging the orbitals obtained from a calculation with the underlying semilocal functional Exc SL into the total-energy hybrid functional. By doing so, the 2nd variational Hamiltonian is not calculated and therefore the computational time will be reduced. After having done and saved a well converged calculation with the semilocal functional, the setting up of a non-self-consistent calculation is the same as for a self-consistent calculation (see above), but with the additional switch -nonself (-hf and -i 1 will be set automatically) that has to be used in run(sp) lapw : run(sp) lapw -nonself... This option can be particularly interesting for the calculation of the lattice constant, which depends mainly on the functional, but very little on the orbitals plugged into the functional. It can be used simultaneously with the option -diaghf (see above). Starting a calculation from another k-mesh Due to the orbital-dependence of the HF potential, it is not straightforward to start directly a calculation with a potential generated from a previous calculation with another k-mesh. However, due to the high cost of a hybrid calculation, it is desirable to have this possibility in order to reduce the number of iterations during the scf procedure. This option is also useful if a vector file on a very dense k-mesh is needed, e.g. for optics or transport properties (BoltzTraP), while using such a k-mesh for a full self-consistent calculation would not be necessary (and would be too expensive). In this case you want to do only one iteration (-i 1). The procedure is the following: Do the calculation with the first k-mesh and save it when it is finished (do not execute clean lapw since case.vectorhf should be present). cp case.klist fbz case.klist fbz old cp case.klist rfbz case.klist rfbz old (if the option -redklist is also used) Execute run kgenhf lapw to create the files for the new k-mesh. Run the HF calculation with -newklist: run(sp) lapw -hf -newklist (-i 1)... This option can be used simultaneously with -redklist but not with -diaghf (see above). Band structure plotting In order to make a plot of the band structure with hybrid functionals, it is more convenient to use the program run bandplothf lapw. After the self-consistent calculation is finished and saved (do not execute clean lapw since case.vectorhf must be present), do the following steps: Create case.klist band. Execute run bandplothf lapw with one or several of the following flags that were also used during the self-consistent calculation: -up/dn, -diaghf, -redklist and -in1orig. Note that a parallel calculation of the band structure (with -p) can be done even if the scf calculation was not done in parallel (but you still need a file.machines). You can also use -qtl to calculate the partial charges for band character plotting. Create case.insp.

72 54 CHAPTER 4. FILES AND PROGRAM FLOW Execute x spaghetti with the switch -hf. First, run bandplothf lapw calculates the semilocal orbitals (x lapw1 -band) for the k-points in case.klist band. Then, the hybrid eigenvalues at these k-points are calculated (x hf -band). If -qtl is used, then the partial charges will be calculated (x lapw2 -band -qtl). Density of states The calculation of the DOS is the same as for the semilocal functionals, but using the additional flag -hf when executing lapw2 for the partial charges (x lapw2 -qtl -hf) and tetra for the DOS (x tetra -hf) modified Becke-Johnson potential (mbj) for band gaps The modified Becke-Johnson exchange potential + LDA-correlation (Tran and Blaha 2009) allows the calculation of band gaps with an accuracy similar to very expensive GW calculations. It is a semilocal approximation to an atomic exact-exchange potential and a screening term. This is just a XC-potential, not a XC-energy functional, thus E xc is taken from LSDA and the forces cannot be used with this option. We recommend the following steps to perform a mbj calculation (the purpose of the first five steps is just only to create the starting case.r2v and case.vresp files): run a regular initialization and SCF calculation using LDA or PBE (it does not matter at all which functional you choose). init mbj lapw. This performs automatically the following steps: create case.inm vresp (cp $WIENROOT/SRC templates/template.inm vresp case.inm vresp. edit case.in0 and set R2V option (instead of NR2V ) such that the XC potential is written in case.r2v. run one more iteration (use run lapw -NI -i 1) to generate the required case.r2v and case.vresp files. save the LDA (or PBE) calculation. run init mbj lapw again. The second call (once case.inm vresp is present) will do the following steps: edit case.in0 and change the functional to option XC MBJ (indxc=28) (this is mbj). cp case.in0 case.in0 grr and choose EX GRR VX GRR (indxc=50) in case.in0 grr. This option will calculate the average of ρ/ρ over the unit cell. (The presence of case.in0 grr will be detected during the SCF procedure and lapw0 will be called twice, first with the input file case.in0 grr, then with case.in0.) select a specific mbj parametrization (see below) and creates the corresponding file case.in0abp. Eventually, edit case.inm and choose the PRATT mixing scheme. run the mbj SCF calculation. It could well be that the default mixing scheme leads to convergence problems (this is what we have observed in many cases). The reason is that the mbj potential also depends on the kinetic energy density which is not mixed in mixer. If such a convergence problem appears, you have to use the PRATT mixing. The PRATT mixing can be slow, lead to oscillations or even lead to divergence. Thus, first you should use a smaller mixing factor (eg. 0.2 or 0.1) and later (when the calculation approaches convergence) increase it to about 0.40 to make sure that your calculation

73 4.5. FLOW OF PROGRAMS 55 did not stop at a false (pseudo) convergence. In most cases it is also possible to switch back to MSR1 after some initial (typical 5-10) scf-cycles. The mbj potential uses an average of ρ/ρ over the unit cell. This does not make sense for surfaces or molecules. In such cases, run a similar bulk structure first, then cp case bulk.grr to case.grr and remove case.in0 grr. This runs mbj with a fixed value of c. If you want to use other mbj parameters than those defined in (Tran and Blaha 2009), eg. the optimized values of (Koller et al. 2012) you can define them during init mbj lapw or directly in case.in0abp. Put 3 values A, B, e (default=-0.012, 1.023, 0.5), which determines the parameter c in mbj according to eq. 7 or Table II. in (Koller et al. 2012) DFT-D3 for dispersion energy dftd3 calculates the dispersion energy and forces using the semi-empirical DFT-D3 method of Grimme et al Since this method depends only on the positions of atoms (no dependence on the electron density) it is very fast and adds very little computer time. The dftd3 package is not included by default in WIEN2k, but can be downloaded from the website of the group of S. Grimme When compilation is done, the executable dftd3 has to be copied in the $WIENROOT directory. run(sp) lapw has to be executed with the -dftd3 switch: run(sp) lapw -dftd3 The user can either create the input file case.indftd3 (described in Sec ) by hand or let run(sp) lapw copy the default one from $WIENROOT/SRC templates/. The dftd3 package requires the file case.poscar (or case.xyz if periodic boundary conditions are switched off) created by the utility program struct2poscar, which is run automatically by run(sp) lapw. The DFT-D3 method contains parameters which are specific to the exchange-correlation functional to which the dispersion energy is added. The functionals available in WIEN2k for which such parameters are available are the GGAs PBE, PBEsol, revpbe, RPBE, and BLYP, the MGGA TPSS, the GGA-hybrids PBE0, B3LYP, B3PW91 and HSE06 (corresponding to YS-PBE0 in WIEN2k) and the MGGA-hybrids TPSSh and TPSS0. More detailed informations on the DFT-D3 method and available options are given in Sec. 7.2 and in the file man.pdf included in the dftd3 TAR file.

74 56 CHAPTER 4. FILES AND PROGRAM FLOW

75 5 Shell scripts for running programs Contents 5.1 Job control Utility scripts Structure optimization Phonon calculations Parallel Execution Chemical shift NMR calculations Wannier functions (wien2wannier) Spontaneous Polarization, Piezoelectricity and Born Charges (BerryPI) Getting on-line help Interface scripts Job control (c-shell scripts) In order to run WIEN2k several c-shell scripts are provided which link the individual programs to specific tasks. All available (user-callable) commands have the ending lapw so you can easily get a list of all commands using ls $WIENROOT/ lapw in the directory of the WIEN2k executables. (Note: all of the more important commands have a link to a short name omitting lapw.) All these commands have at least one option, -h, which will print a small help indicating purpose and usage of this command Main execution script (x lapw) The main WIEN2kscript, x lapw or x, executes a single WIEN2kprogram. First it creates the corresponding program.def-file, where the connection between Fortran I/O-units and filenames are defined. One can modify its functionality with several switches, modifying file definitions in case of spin-polarized or complex calculations or tailoring special behaviour. All options are listed with the help switch x -h or x lapw -h With some of the options the corresponding input files may be changed temporarely, but are set back to the original state upon completion. 57

76 58 CHAPTER 5. SHELL SCRIPTS USAGE: x PROGRAMNAME [flags] PURPOSE:runs WIEN executables: afminput,aim,arrows,broadening,cif2struct, clmaddsub,clmcopy,clminter,convham,conv2prim,dftd3,dipan,dmftproj, dstart,eosfit,eosfit6,filtvec,findbands,fleur2wien,hex2rhomb,hf, initxspec,irrep,joint,joinvec,kgen,kram,lapw0,lapw1,lapw2, lapw3,lapw5,lapw7,lapwdm,lapwso,lcore,lorentz,lstart,mini,mixer,nn, optimize,orb,pairhess,plane,rhomb_in5,sgroup,shifteig,spaghetti, struct2cif,struct2poscar,struct_afm_check,sumpara,supercell,symmetry, symmetso,telnes3,tetra,txspec,wannier90,w2w,w2waddsp,wplot,xspec FLAGS: -f FILEHEAD -> FILEHEAD for path of struct & input-files -t/-t -> suppress output of running time -h/-h -> help -d -> create only the def-file -up -> runs up-spin -dn -> runs dn-spin -du -> runs up/dn-crossterm -sc -> runs semicore calculation -c -> complex calculation (no inversion symmetry present) -p -> run lapw0/1/2/hf/so/dm/optic/dstart in parallel (needs.machines or.processes file) -scratch dir/ ->defines (and makes) $SCRATCH variable -grr -> lapw0 for mbj or hf (using $file.in0_grr) -eece -> for hybrid-functionals (lapw0,lapw2,mixer,orb,sumpara) -band -> for lapw1/2/hf bandstructures: uses *klist_band -orb -> runs lapw1 with LDA+U/OP or B-ext correction, mixer with dmat -it -> runs lapw1 with iterative diagonalization -nohinv -> runs lapw1 with iterative diag. without Hinv -nohinv0 -> runs lapw1 with iterative diag. writing new Hinv -nohns-> runs lapw1 without HNS -nmat_only-> runs lapw1 and yields only the matrixsize -nmr -> runs lapw1 in NMR mode -in1orig -> runs lapw2 but does not modify case.in1 -emin X -> runs lapw2 with EMIN=X (in bin9_blaha.in2) -all X Y -> runs lapw2 with ALL and E-window X-Y (in bin9_blaha.in2) -qtl -> runs lapw2 and calculates QTL -alm -> runs lapw2 and calculates ALM,BLM -almd -> runs lapw2 and calculates ALM,BLM in lapw2 for DMFT (Aichhorn) -qdmft -> runs lapw2 and calculates charges including DMFT (Aichhorn) -help_files -> runs lapw2 and creates case.helpxx files -vresp-> runs lapw2 and creates case.vrespval (for TAU/meta-GGA) -fermi-> runs lapw2 with FERMI switch -efg -> runs lapw2 with EFG switch -so ->runs lapw2/optic/spaghetti with def-file for spin-orbit calc. -hf -> runs lapw2 with Hartree-Fock/hybrid vectors -diaghf -> calculates only the diagonal elements of HF Hamiltonian -nonself -> calculates hf with Ex only (no eigenvalues/vectors) -fbz ->runs kgen and generates a full mesh in the BZ -fft -> runs dstart only up to case.in0_std creation -super-> runs dstart and creates new_super.clmsum (and not $file.clmsum) -lcore-> runs dstart with $file.rsplcore (produces $file.clmsc) -sel -> use reduced vector file in lapw7 -settol 0.000x -> run sgroup with different tolerance -sigma-> run lstart with case.inst_sigma (autogenerated) for diff.dens. -rxes-> run tetra using case.rxes weight file for RXES-spectroscopy. -rxesw E1 E2-> run tetra and create case.rxes file for RXES for energies E1-E2 -enefile -> spaghetti+tetra with case.energy instead case.qtl (only tot-dos) -delta-> run arrows program with difference between two structures -copy -> runs pairhess and copies.minpair to.minrestart and.minhess -telnes -> run qtl after generating case.inq based on case.innes -txt -> runs cif2struct using case.txt (see UG) -pp -> run wannier90 in "preprocessing mode" -wf N -> run wplot for Wannier function N -efermi EF -> run findbands (unit:ryd) / shifteig (unit:ev) with Fermi energy EF -emax Y -> for findbands USE: x -h PROGRAMNAME for valid flags for a specific program Note: To make use of a scratch file system (usually a local file system for reducing the network or central fileserver load), you may specify such a filesystem in the environment variable SCRATCH (it may already have been set by your system administrator and must exist on all your nodes) or using the -scratch switch (directory will be created automatically if it does not exist). However, you have to make sure that there is enough disk-space in the SCRATCH directory to hold your case.vector* and case.help* files.

77 5.1. JOB CONTROL Create the master input file case.struct (makestruct lapw) The primary input file for a case is called case.struct. It can be created by the Struct Generator of w2web, by some utilities like cif2struct or xyz2struct or using an interactive script makestruct lapw. This script asks for lattice-type or spacegroup, atoms and their positions, and produces an intermediate file datastruct. The auxilliary programs Tmaker and setrmt lapw converts this into init.struct, which must be copied to the proper location/filename by the user. makestruct lapw was provided by Morteza Jamal (m and Peter Blaha Job control for initialization (init lapw) In order to start a new calculation, one should make a new subdirectory and run all calculations from there. At the beginning one must provide at least one file (see quick-start 3 or the makestruct lapw script5.1.2), namely case.struct (see 4.3). (case.inst can be created automatically on the fly, see 6.4.3), then one runs a series of programs using init lapw. This script is described briefly in chapter 4.5) and in detail in Getting started for the example TiC (see chapter 3). You can get help with switch -h. All actions of this script are logged in short in :log and in detail in the file case.dayfile, which also gives you a restart option when problems occurred. In order to run init lapw starting from a specific point on, specify -s PROGRAM. Ignoring ERRORS and in many cases also WARNINGS during the execution of this script, most likely will lead to errors at a later stage. Neglecting warnings about core-leakage creates.lcore, which directs the scf-cycle to peform a superposition of core densities. init lapw supports switch -b, a batch mode (non-interactive) for trivial cases AND experienced users. You can supply various options and specify spin-polarization, XC-potential, RKmax, k-mesh or mixing. See init lapw -h for more details. Changes to case.struct by nn will be accepted, but by sgroup will be neglected. Please check the terminal output for ERRORS and WARN- INGS!!! Job control for iteration (run lapw or runsp lapw) In order to perform a complete SCF calculation or even perform both, a optimization of internal atomic positions and a SCF calculation simultaneously, several types of scripts are provided with the distribution. For the specific flow of programs see chapter 4.5. For more information on atomic position optimization see chapter For non-spinpolarized calculations use: run lapw, for spin-polarized calculations use: runsp lapw. for antiferromagnetic calculations use: runafm lapw for FSM (fixed-spin moment) calculations use: runfsm lapw for a spin-polarized setup, where you want to constrain the moment to zero (e.g. for LDA+U calculations) use: runsp c lapw Cases with/without inversion symmetry and with/without semicore or core states are handled automatically by these scripts. All activities of these scripts are logged in short in :log (appended) and in detail together with convergence information in case.dayfile (overwriting the old dayfile ). You can always get help on its usage by invoking these scripts with the -h flag. run lapw -h

78 60 CHAPTER 5. SHELL SCRIPTS PROGRAM: PURPOSE: USAGE: /zeus/lapw/wien2k/bin/run_lapw running the nonmagnetic scf-cycle in WIEN to be called within the case-subdirectory has to be located in WIEN-executable directory run_lapw [OPTIONS] [FLAGS] OPTIONS: -cc LIMIT -> charge convergence LIMIT ( e) -ec LIMIT -> energy convergence LIMIT ( Ry) -fc LIMIT -> force convergence LIMIT (1.0 mry/a.u.) default is -ec ; multiple convergence tests possible -e PROGRAM -> exit after PROGRAM () -i NUMBER -> max. NUMBER (40) of iterations -s PROGRAM -> start with PROGRAM () -r NUMBER -> restart after NUMBER (99) iterations (rm *.broyd*) -nohns NUMBER ->do not use HNS for NUMBER iterations -in1new N -> create "new" in1 file after N iter (write_in1 using scf2 info) -ql LIMIT -> select LIMIT (0.05) as min.charge for E-L setting in new in1 -qdmft NP -> including DMFT from Aichhorn/Georges/Biermann running on NP proc -scratch dir/ -> sets (and creates) scratch directory (for vector files) FLAGS: -h/-h -> help -I -> with initialization of in2-files to "TOT" -NI -> does NOT remove case.broyd* (default: rm *.broyd* after 60 sec) -p -> run k-points in parallel (needs.machine file [speed:name]) -it -> use iterative diagonalizations -it1 -> use iterative diag. with recreating H_inv (after basis change) -it2 -> use iterative diag. with reinitialization (after basis change) -nohinv -> use iterative diag. without H_inv -vec2pratt -> use vec2pratt instead of vec2old for iterative diag. -so -> run SCF including spin-orbit coupling -renorm-> start with mixer and renormalize density -in1orig-> if present, use case.in1_orig file; do not modify case.in1 -hf -> HF/hybrid-DFT calculation -diaghf -> non-selfconsistent HF with diagonal HF only (only e_i) -nonself -> non-selfconsistent HF/hybrid-DFT calculation (only E_x(HF)) -newklist -> HF/hybrid-DFT calculation starting from a different k-mesh -reklist -> HF/hybrid-DFT calculation with a reduced different k-mesh for -dftd3 -> include the dispersion energy and forces with the DFT-D3 method -min -> force optimization using MSR1a CONTROL FILES:.lcore.stop.minstop.fulldiag.noHinv case.inm_vresp case.in0_grr runs core density superposition producing case.clmsc stop after SCF cycle in MSR1A mode(structure optimization) switches to MSR1 force full diagonalization remove case.storehinv files activates calculation of vresp files for meta-ggas activates a second call of lapw0 (mbj pot., or E_xc analysis) ENVIRONMENT VARIBLES: SCRATCH directory where vectors and help files should go Additional flags valid only for magnetic cases (runsp lapw) include: -dm -> calculate the density matrix (when -so is set, but -orb is not) -eece -> use "exact exchange+hybrid" methods -orb -> use LDA+U, OP or B-ext correction -orbc -> use LDA+U correction, but with constant V-matrix Calling run lapw (after init lapw) from the subdirectory case will perform up to 40 iterations (or what you specified with switch -i) unless convergence has been reached earlier. You can choose from three convergence criteria, -ec (the total energy convergence is the default and is set to Ry for at least 3 iterations), -fc (magnitude of force convergence for 3 iterations, ONLY if your system has free structural parameters!) or -cc (charge convergence, just the last iteration), and any combination can also be specified. Be careful with these criteria, different systems will require quite different limits (e.g. fcc Li can be converged to µry, a large unit cell with heavy magnetic atoms only to 0.1 mry). You can stop the scf iterations after the current cycle by generating an empty file.stop (use eg. touch.stop in the respective case-directory).

79 5.1. JOB CONTROL 61 The scf-cycle creates case.broyd* files which contain the charge-history. Once run lapw has finished, you should usually save lapw (see below) the results. When you continue with another run lapw without save lapw (because the previous run did not fulfill the convergence criteria or you want to specify a more strict criterium) the broyden-files will be deleted unless you specify -NI. With -e PROGRAM you can run only part of one scf cycle (e.g. run lapw0, lapw1 and lapw2), with -s PROGRAM you can start at an arbitrary point in the scf cycle (e.g. after a previous cycle has crashed and you want to continue after fixing the problem) and continue to self-consistency. Before mixer is invoked, case.clmsum is copied to case.clmsum old, and the final important files of the scf calculation are case.clmsum and case.scf. Invoking run lapw -I -i 30 -fc 0.5 will first set in case.in2 the TOT-switch (if FOR was set) to save cpu time, then run up to 30 scf cycles till the force criterion of 0.5 mry/a.u. is met (for 3 consecutive iterations). Then the calculation of all terms of the forces is activated (setting FOR in case.in2) for a final iteration. An additional switch -min will activate the optimization of the internal positions using the MSR1a option in case.inm (see Sec ). Note, this option can take several hundreds of scf-cycles in more complicated cases. By default the file case.in1 is updated after lapw2 and the current Fermi-energy is inserted. This will force lapw1 to use instead of the default energy parameters (0.30) an energy E F 0.2. The switch -in1orig can be used to keep the present case.in1 file unmodified (or to copy case.in1 orig back after -in1new). The switch -in1new N preserves for N iteration the current case.in1 file. After the first N iterations write in1 lapw is called and a new case.in1 file is generated, where the energy parameters are set according to the :EPLxx and :EPHxx values of the last scf iteration and the -ql value (see sections 4.4 and 7.5). In this way you may select in some cases better energy-parameters and also additional LOs to improve the linearization may be generated automatically. Note, however, that this option is potentially unsave and dangerous, since it may set energy-parameters of LOs and APW+lo too close (leading to ghostbands) or in cases where you have a bad last iteration (or large changes from one scf iteration to the next. The original case.in1 file is saved in case.in1 orig and is used as template for all further scf-cycles. Parallelization is described in Sec Iterative diagonalization, which can significantly save computer time (in particular for cases with few electrons (like surfaces) and large matrices (larger than 2000) a factor 2-5! is possible), is described in Sec It needs the case.vector.old file from the previous scf-iteration (and this file is created from case.vector when the -it switch is set) and an inverse of a previous Hamiltonian (H0 1 ) stored in case.storehinv. When you change the Hamiltonian significantly (changing RKmax or local orbitals), reinitialize the iterative diagonalization either by touch.fulldiag (performs one full diagonalization) or touch.nohinv (recreates case.storehinv files) or using the -it1 -it2 switch. You can save computer time by performing the first scf-cycles without calculating the non-spherical matrix elements in lapw1. This option can be set for N iterations with the -nohns N switch. The presence of the file.lcore directs the script to superpose the radial core densities using dstart and generating case.clmsc. It is created automatically during init lapw when chargeleakage warnings are ignored. This option allows to reduce the number of semi-core states, but still keeping a good charge density. dstart can also run in mpi-parallel mode, otherwise it can be slow for big cases.

80 62 CHAPTER 5. SHELL SCRIPTS The presence of the file case.in0 grr activates a second call of lapw0, which is necessary for modified Becke-Johnson potentials (see Section 4.5.9) or E xc analysis. It is also possible to calculate exact exchange (Hartree-Fock) and perform full hybrid-dft calculations. However, such calculations are very expensive. They are activated using the -hf switch. More information can be found in Sec If you have a previous scf-calculation and changed lattice parameters or positions (volume optimization or internal positions minimization), one could use -renorm to renormalize the density prior to the first iteration., but the recommended way is to use clmextrapol lapw. For magnetic systems which are difficult to converge you can use the script runfsm lapw -m M (see section 4.5.3) for the execution of fixed-spin moment (FSM) calculations. 5.2 Utility scripts Save a calculation (save lapw) After self-consistency has been reached, the script save lapw head of save filename saves case.clmsum, case.scf, case.dmat, case.vorb and case.struct as well as all inputs (case.in* under the new name and removes the case.broyd* files. Now you are ready to modify structural parameters or input switches and rerun run lapw, or calculate properties like charge densities (lapw5), total and partial DOS (tetra) or energy bandstructures (spaghetti). For more complicated situations, where many parameters will be changed, we have extended save lapw so that calculations can not only be saved under the head of save filename but also a directory can be specified. If you use any of the possible switches (-o, -f, -d, -s) all input files will be saved as well (and can be restored using restore lapw). Options to save lapw can be seen with save lapw -h Currently the following options are supported -h help -o old scheme, does not save input files -f force save lapw to overwrite previous saves of the same name -d directory save calculation in directory specified -s silent operation (no output on screen) -dos saves case.int, qtl and dos files -band saves case.output1/so, qtl, irrep and spaghetti files -optic saves case.symmat,joint,epsilon,sigma,eloss,absorp,klist,kgen,inop,injoint,inkram... files Note: for DOS, bandstructure or optic, there is no corresponding restore lapw option, but files must be handled by hand Restoring a calculation (restore lapw) To restore a calculation the script restore lapw can be used. This script restores the struct, clmsum, vorb and dmat files as well as all input files. Note: The input files will only be restored when save lapw -d was used, i.e. when you have saved a calculation in an extra directory.

81 5.2. UTILITY SCRIPTS 63 After restore lapw you can continue and either run an scf cycle (run lapw) or recreate the scf-potential (x lapw0) and the corresponding eigenvectors (x lapw1) for further tasks (DOS, electron density,...). Options to restore lapw are: -h help -f force restore lapw to overwrite previous files -d directory restore calculation from directory specified -s silent operation (no output) -t only test which files would be restored Reduce atomic spheres and interpolate density (reduce rmt lapw) reduce rmt lapw [ -r XX -up] When a structure optimization (MSR1a and run(sp) lapw or min lapw) fails because of overlapping spheres, this script will reduce the spheres (default: 3 % or use -r XX) and interpolate the density inside the spheres to the new radial mesh. Setting the switch -up will do it for clmsum, clmup and clmdn files Remove unnecessary files (clean lapw) Once a case has been completed you can clean up the directory with this command. Only the most important files (scf, clmsum, struct, input and some output files) are kept. It is very important to use this command when you have finished a case, since otherwise the large vector and helpxx files will quickly fill up all your disk space. Options to clean lapw are: -h help -s silent operation (no output) -r recursively clean all directories starting from the current one Migrate a case to/from a remote computer (migrate lapw) This script migrates a case to a remote computer (to be called within the case-dir). Needs working ssh/scp without password; local and remote case-dir must have the same name. Call it within the desired case-dir as: migrate lapw [FLAGS OPTIONS] with the following options: -put -get -all -start -end -save savedir -> transfer of files to a remote host (default) -> transfer of files from a remote host -> the complete directory is copied -> only files to start an scf cycle are copied (default for put) -> only new files resulting from an scf cycle are copied (default for get) -> "save_lapw -d save_dir" is issued and only save_dir is copied FLAGS: -h -> help

82 64 CHAPTER 5. SHELL SCRIPTS -clean -> a clean_lapw is issued before copying -r -> files in source directory are removed after copying -R -> source directory (and all files) are removed after copying -s -> do it silent (in batch mode) -z -> gzip files before scp (slow network) Generate case.inst (instgen lapw) This script generates case.inst from a case.struct file. It is used automatically in init lapw, if case.inst is not present. Using some options (see below) it allows to define the spin-state of all/certain atoms. Note: the label RMT is necessary in case.struct. instgen_lapw [-h -s -up -dn -nm -ask] -h: generate this message -s: silent operation (do not ask) -up: generates spin-up configuration for all atoms (default) -dn: generates spin-dn configuration for all atoms -nm: generates non-magnetic configuration for all atoms -ask: asks for each atom which configuration it should generate Set R-MT values in your case.struct file (setrmt lapw) This perl-script executes x nn and uses its output to determine the atomic sphere radii (obeying recommended ratios for H, sp-, d- and f- elements). It is called automatically within init lapw or you may call it in the or explicitly using: setrmt lapw case [-r X ] [-a XX:A,YY:B,... ] [-orig] where case gives the head of the case.struct file. You may specify a reduction (-r) of the RMTs by X percent in order to allow for structural optimizations. If you already know which RMT values you want to know for a certain element, you can fix them using eg. (-a Mg:1.9). The new setrmt lapw version knows optimal RKmax values for all atoms and makes a finer tuning of the different RMTs. with (-orig) you can go back to the old scheme which distinguishes only between H, sp- and d-elements. It creates case.struct setrmt with the modified RMTs create add atom clmsum lapw The script create add atom clmsum lapw creates a better starting density for a case, where you alsready have a scf-solution for a similar case. Similar means, that the new and old case are identical except for ONE atom (adding an adsorbate,...). This script is experimental and only for experienced users. It is usefull in BIG cases, which are difficult to converge from init lapw. Modifications and adaptions to a specific case are probably necessary Create case.int file (for DOS) (configure int lapw) This script creates the input file case.int for the program tetra and allows to specifiy which partial DOS (atom, l and m) should be calculated. It was provided by Morteza Jamal (m You can specify interactively:

83 5.2. UTILITY SCRIPTS 65 total (for plotting Total Dos ) N (to select atom N) s,p,d,... (to select a set of PDOS for previously selected atom N) use labels as listed in the header of your case.qtl file) end (for exit) There is also a batch (non-interactive) mode: configure_int_lapw -b total 1 tot,d,d-eg,d-t2g 2 tot,s,p end which will prepare case.int (eg. for the TiC example) with: tic #Title #Emin, DE, Emax, Gauss-Broad 8 #Number of DOS 0 1 total-dos 1 1 tot-ti 1 4 d-ti 1 5 d-eg-ti 1 6 d-t2g-ti 2 1 tot-c 2 2 s-c 2 3 p-c Check for running WIEN jobs (check lapw) This script searches for.running.* files within the current directory (or the directory specified with -d full path directory ) and then performs a ps command for these processes. If the specified process has not been found, it removes the corresponding.running.* file after confirmation (default) or immediately (when -f has been specified) Cancel (kill) running WIEN jobs (cancel lapw) This script searches for.running.* files within the current directory (or the directory specified with -d full path directory ) and then kills the corresponding process after confirmation (default) or immediately (when -f has been specified). It is particular useful for killing k-point parallel jobs Extract critical points from a Bader analysis (extractaim lapw) This script extracts the critical points (CP) after a Bader analysis (x aim (-c)) from case.outputaim. It sorts them (according to the density), removes duplicate CPs, converts units into Å, e/å 3,... and produces critical points ang. It is used with: extractaim lapw case.outputaim scfmonitor lapw This program was contributed by:

84 66 CHAPTER 5. SHELL SCRIPTS Hartmut Enkisch Institute of Physics E1b University of Dortmund Dortmund, Germany Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. It produces a plot of some quantities as function of iteration number (a maximum of 6 quantities is possible at once) from the case.scf file as specified on the commandline using analyse lapw and GNUPLOT. This plot is updated in regular intervals. You can call scfmonitor lapw using: scfmonitor lapw [-h] [-i n] [-f case.scf] [-p] arg1 [arg2.. arg6] -h help switch -i n show only the last n iterations -f scf-file use "scf-file" instead of the default "case.scf" -p produces file "scfmonitor.png" instead of X-window plot arg1,... arguments to monitor (like ":ENE" or ":DIS", see analyse_lapw ) The scfmonitor can also be called directly from w2web using the Analyse tool. In order to have a reasonable behavior of scfmonitor the GNUPLOT window should stay in background. This can be achieved by putting a line into your.xdefaults file like: gnuplot*raise: off Note: It does not make sense to start scfmonitor before the first cycle has finished because no case.scf exists at this point analyse lapw The script analyse lapw is usually called from scfmonitor lapw. It greps from an scf-file the specified arguments and produces analyse.out. analyse lapw is called using: analyse lapw [-h] scf-file arg1 [arg2 arg3 arg4 arg5 arg6] -h help switch scf-file "scf-file" to analyse (there s no default "case.scf"!) arg1,... arguments to analyse: atom independent: :ENE :DIS :FER :MMT :VOL :GAP atom iii dependent: :CTOiii :CUPiii :CDNiii :NTOiii :NUPiii :NDNiii :DTOiii :DUPiii :DDNiii :RTOiii :EFGiii :HFFiii :MMIiii vector quantities: :FORiii[x/y/z] :POSiii[x/y/z] :FGLiii[x/y/z] where magnitude z z is the default For vector quantities like :FGLiii or :POSiii (useful with case.scf mini) one can specify the respective coordinate by adding x/y/z to the corresponding labels.

85 5.2. UTILITY SCRIPTS Check parallel execution (testpara lapw) testpara lapw is a small script which helps you to determine an optimal selection for the file.machines for parallel calculations (see sec. 5.5) Check parallel execution of lapw1 (testpara1 lapw) testpara1 lapw is a small script which determines how far the execution of lapw1para has proceeded Check parallel execution of lapw2 (testpara2 lapw) testpara2 lapw is a small script which determines how far the execution of lapw2para has proceeded grepline lapw Using grepline lapw :label filename*.scf lines for tail or grepline :label filename*.scf lines for tail you can get a list of a quantity :label (e.g. :ENE for the total energy) from several scf files at once initso lapw initso lapw helps you to initialize the calculations for spin-orbit coupling. It helps together with make inso lapw (based on an idea of Morteza Jamal, m to create/modify all required input files (case.inso, case.in1, case.in2c). In a spinpolarized case SO may reduce symmetry or equivalent atoms may become non-equivalent, and the script calls symmetso and will help you to find proper symmetries and setup the respective input files. It is called using initso lapw or initso and you should carefully follow the instructions and explanations of the script and the explanations for case.inso given in section 7.6. Since forces are not correct for atoms with SO, it can be very useful to suppress SO for light atoms (eg. the O-atoms in UO 2 ), because then one can optimize the O-positions init hf lapw init hf lapw helps you to initialize the calculations for hybrid-dft functionals. It creates several files (case.inhf, case.in0 grr), selects YS-PBE0 (see Ref. Tran,Blaha 2011), changes some input files (case.in0) and calls run kgenhf lapw to generate the k-mesh for the HF calculation. It takes -up for spin-polarized cases. For details of hybrid-dft calculations see

86 68 CHAPTER 5. SHELL SCRIPTS init mbj lapw init mbj lapw helps you to initialize the calculations for a TB-mBJ (see Tran, Blaha 2009) calculation, which usually requires a couple of steps done in proper order. A proper sequence would be: init mbj lapw run lapw -i 1 init mbj lapw save lapw xxxx pbe run lapw The first call to init mbj lapw creates case.inm vresp and sets R2V in case.in0. The second call of init mbj lapw creates case.in0 and case.in0 grr with the proper input for mbj. It also lets you select parameters of the original TB-mBJ potential, or the later adaption to semiconductors or insulators, or the original BJ method. For details of TB-mBJ calculations see vec2old lapw vec2old lapw moves case.vector files to case.vector.old. Usually called automatically just before lapw1 when the iterative diagonalization (run lapw -it) is specified. It also works for the k-parallel case including local $SCRATCH directories (add -p as first argument, uses hosts from.processes and requires commensurate k-point/number of processors) and spinpolarization (-up/-dn switches). For runfsm lapw the sequence had to be changed and the switches -updn or -dnup forces vec2old to COPY case.vectorup tocase.vectordn (and vice versa). In the runfsm lapw case the corresponding case.vector*.old files are generated just AFTER lapw2/lapwdm and not BEFORE lapw1. Thus after runfsm lapw has finished, the corresponding spin-up/dn vectors are case.vector*.old and NOT case.vector*. The switches -p -local will copy $SCRATCH/case.vector* to case.vector*. It will be done automatically when you run x lapw2 -p -qtl. An alternative script vec2pratt lapw was provided by L.D.Marks which together with SRC vecpratt mixes the last two vectors (Pratt mixing) to generate case.vector.old. It is activatd using the -vec2pratt switch in run lapw clmextrapol lapw clmextrapol lapw extrapolates the charge density (case.clmsum/up/dn) from old to new positions (or from old to new lattice parameters). It takes the density from the old positions (copied into old.clmsum) and subtracts an atomic superposition density (new super.clmsum) fom the old positions and adds an atomic superposition density fom the new ones (generated by dstart). If new super.clmsum (generated automatically by init lapw) is not present, it will be generated and for the next geometry step an extrapolation will take place. It is usually called from min lapw after a geometry step has finished and a new struct file has been generated. It can significantly reduce the number of scf-cycles for the new geometry step.

87 5.3. STRUCTURE OPTIMIZATION makescratch lapw makescratch lapw scratch-dir-name checks the existense of the directory and eventually creates it (up to 3 levels deep). Usually called automatically by other Wien2k-scripts. 5.3 Structure optimization Lattice parameters (Volume, c/a, lattice parameters) Package optimize The auxilliary program optimize (x optimize) generates from an existing case.struct (or case initial.struct, which is generated at the first call of optimize) a series of struct files with various volumes (or c/a ratios, or other modified parameters) (depending on your input): [1] VARY VOLUME with CONSTANT RATIO A:B:C [2] VARY C/A RATIO with CONSTANT VOLUME (tetr and hex lattices) [3] VARY C/A RATIO with CONSTANT VOLUME and B/A (orthorh lattice) [4] VARY B/A RATIO with CONSTANT VOLUME and C/A (orthorh lattice) [5] VARY A and C (2D-case) (tetragonal or hexagonal lattice) [6] VARY A, B and C (3D-case) (orthorhombic lattice) [7] VARY A, B, C and Gamma (4D-case) (monoclinic lattice) [8] VARY C/A RATIO and VOLUME (2D-case) (tetr and hex lattices) It also produces a shell-script optimize.job which looks similar to: #!/bin/csh -f foreach i ( \ tic_vol_-10.0 \ tic_vol -5.0 \ tic_vol 0.0 \ tic_vol 5.0 \ tic_vol 10.0 \ ) cp $i.struct tic.struct # cp $i.clmsum tic.clmsum # x dstart # run_lapw -ec in1new 3 -renorm run_lapw -ec set stat = $status if ($stat) then echo "ERROR status in" $i exit 1 endif save_lapw ${i} # save_lapw -f -d XXX $i end You may modify this script according to your needs: use runsp lapw or even min lapw, or specify different convergence parameters; modify the save lapw command and change the save-name or save into a directory to separate e.g. gga and lda results. Eventually you may activate the line cp $i.clmsum case.clmsum to use a previously saved clmsum file, e.g. from a calculation with smaller RKmax,... and deactivate the clmextrapol lapw lines, but usually the latter is so efficient that this is no longer recommended. Note: You must have a case.clmsum file (either from init lapw or from a previous scf calculation) in order to run optimize.job. After execution of this script you should have a series of scf-files with energies corresponding to the modified parameters, which should allow you to find the corresponding equillibrium parameters. For the volume optimization an analysis tool is available, other tools are under development). Using the script grepline (or the Analysis Analyze multiple SCF-files menu of w2web) you get a summary of the total energy vs. volume (c/a). The file case.analysis can be used in

88 70 CHAPTER 5. SHELL SCRIPTS eplot lapw or gibbs lapw to find the minimum total energy and the equilibrium volume (or c/a or b/a). Supported equation of states include the EOS2, Murnaghan and Birch-Murnaghan EOS. grepline :ENE *.scf 1 > case.analysis grepline :VOL *.scf 1 >> case.analysis Alternatively you can also use eplot lapw directly and the case.analysis file is generated automatically : or eplot lapw -a vol eplot -a "*" will analyse all scf files *vol*.scf eplot -a pbe will analyse all scf files *vol*pbe.scf Using such strategies also higher-dimensional optimizations (e.g. c/a ratio and volume) are possible in combination with the -d option of save lapw. For optimization of more degrees of freedom (2-4 lattice parameters), you can use the corresponding option and for analysis of the data the script parabolfit lapw together with the program eosfit6. It performs a non-linear least squares fit, using a parabolic fit-function in your variables and get an analytic description of your energy surface. Please note, this is only a harmonic fit (no odd or higher terms) and the description may not be very good if your parameter range is large and/or the function is quite anharmonic, or you suffer from numerical noise. For the determination of elastic constants see the description of ELAST in sec 8.5 and IRelast in sec 8.8. Package 2DRoptimize This program was contributed by: Morteza Jamal Ghods City-Tehran,Iran m Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. This package [see also Ref. Reshak 2013] performs a convenient 2D structure optimization (Volume and c/a for tetragonal, rhombohedral or hexagonal spacegroups). After initialization of a case, one generates a set of structures and a job-file 2Doptimize.job using the command set2d lapw This calls setup2d and you have to specify the changes in volume and c/a. The resulting 2Doptimize.job script should be adapted (eg. use min lapw instead of run lapw; insert switches,...) and executed. Finally ana2d lapw

89 5.3. STRUCTURE OPTIMIZATION 71 can be executed and will analyze the results. It uses a set of case.vconst* files (produced by 2Doptimize.job and stored also in subdirectory Vconst) and the numbvcoa file. ana2d lapw checks the sensitivity of the results with the order of fitting (3,4 or 5th order polynomials) and lets you select the best one. Note: Fits of high order (and few data points ) may lead to artificial results due to unphysical oszillations of the fit. You can see results for - energy vs. c/a for each volume, - energy vs. volume (with optimized c/a) and - c/a vs. volume. At the end, ana2d lapw calculates a and c lattice constants (and a R, α R for rhombohedral compounds) and checks the sensitivity of them to the order of fit (order of fit=3 or 4 or 5) when it finds the equation of c/a vs. volume and stores in fitorder. Optionally you can specify more cases by rerunning set2d lapw. Specify also your old volume and c/a points again (or leave them out on purpose in case they were very bad (eg. very far from the minimum). The old results will be taken automatically into account without recalculation (unless you modify 2Doptimize.job, see the comments at the top of this file). Thus a good strategy is to use only 3x3 points (order of fit = 3) and in a second step you add points where they are needed. When you want to rerun such an optimization with different parameters (RKmax, k-mesh, XCpotentials) modify the top of 2Doptimize.job and set answscf=no and a new savename (eg. pbe rk8 1000k ) Minimization of internal parameters (min lapw) Most of the more complicated structures have free internal structural parameters, which can either be taken from experiment or optimized using the calculated forces on the nuclei. Starting with WIEN2k 11.1 there are two possibilities to determine the equilibrium position of all individual atoms automatically (obeying the symmetry constraints of a certain space group). One can use either the shell script min lapw, together with the program mini, which will run a scf-cycle, update the positions using the calculated forces and restarts a new scf cycle. This continues until forces drop below a certain value; or use the normal scf-scripts run lapw -min where in case.inm the switch MSR1 will be modified to MSR1a such that the charge density and the positions are simultaneously optimized during the scf-cycle. At present we recommend the second (new) option, although there are cases where this scheme can be slower or may even fail to converge. A typical sequence of commands for an optimization of the internal positions would look like: Generate struct file init lapw run lapw -fc 1 [another runxx script or additional options are of course also possible] (this may take some time) Inspect the scf file whether you have significant forces (usually at least.gt. 5 mry/bohr), otherwise you are more or less at the optimal positions (An experienced user may omit the run lapw step and proceed directly from init lapw to the next step) Now you have to decide which method to use:

90 72 CHAPTER 5. SHELL SCRIPTS min lapw [options] (this may take some time) it will generate a default case.inm (if not present) by: executing x pairhess -copy ; cp case.inm st case.inm (i.e. it sets up the PORT minimization option and calculates an approximate starting Hessian). when -nohess is specified, it will generate case.inm from SRC templates with the NEW1 option (not recommended). Without -NI switch min lapw performs an initialization first: removes histories (case.broyd*, case.tmpm) if present; copies.min hess to.minrestart (if present from previous min lapw or x pairhess). or edit case.inm and put MSR1a (or MSEC1a) as mixing method. save lapw xxx the original calculation and then continue with run lapw -fc 0.5 -ec cc [-it]. It will run x pairhess (unless case.inm is already present) and then run (several hundreds) scf-cycles, simultaneously updating positions and charge densities. Once the forces seem to be smaller than the limit defined in case.inm it will switch to mixing method MSR1 and finalize the scf-cycle with fixed positions. Because of this, the final forces may not be as small as desired and eventually you have to restart this step using MSR1a again. When using the second method we recommend you read carefully $WIEN- ROOT/SRC mixer/readme 5.2.pdf. Overall the method is very good for semiconductors (or well behaved metals), and allows tricks like small k-mesh or small RKMax at the beginning of the minimization and using higher accuracy only towards the end. The following text refers (mainly) to the first method using min lapw: When case.scf is not present, an scf-cycle will be performed first, otherwise the corresponding forces are extracted into case.finm and the program mini generates a new case.struct with modified atomic positions. The previous step is saved under case 1/2/3... Then a new scfcycle is executed and this loop continues until convergence (default: forces below 2mRy/bohr) is reached. The last iteration of each geometry step is appended to case.scf mini, so that this file contains the complete history of the minimization and can be used to monitor the progress (grep :ENE *mini; or :FORxxx...). By default (unless switch -noex is specified), min will call the script clmextrapol lapw after the first geometry step and try to extrapolate the charge density to the new positions. This procedure usually significantly reduces the number of scf-cycles and is thus highly recommended. mini requires an input file case.inm (see Sec. 8.15) which is created automatically and MUST NOT be changed while min lapw is running (except the force tolerance, which terminates the optimization). We recommend the PORT minimization method, a reverse-communication trust-region Quasi- Newton method from the Port library, which seems to be stable, efficient and does not depend too much on the users input (DELTAs, see below with NEWT). The PORT option also uses/produces a file.min hess, which contains the (approximate) Hessian matrix (lower-triangle Cholesky factor) If you restart a minimization with different k-points, RMT, RKmax,... or do a similar calculation (eg. for a different volume,...) it will be copied to.minrestart (unless -nohess is specified), so that you start with a reasonable approximation for the Hessian. The program pairhess, which calculates the first Hessian, also prints out the average Hessian eigenvalue for the symmetric, symmetry-preserving modes in mryd/au2 as well as the minimum and maximum, and also the vibration frequencies. A list of these is given at the end of case.pairhess. Note that these are not all possible modes, but only the symmetry preserving ones. Therefore if you have prior information about the vibrations of the system you can adjust the rescaling term so the average

91 5.3. STRUCTURE OPTIMIZATION 73 vibration frequency is about correct. (see the description of pairhess in 9.2). (In addition there is a program eigenhess, which will analyze the Hessian after the minimization has been completed. It also prints vibrational frequencies and may give you hints about dynamical instability of your system. Some more description is given in $WIENROOT/SRC pairhess/readme and at the top of the output file case.outputeig. When using PORT you may also want to check its progress using grep :LABEL case.outputm where :LABEL is :ENE (should decrease), :GRAD (should also go down, but could sometimes also go up for some time as long as the energy still decreases), :MIN (provides a condensed summary of the progress), :WARN may indicate a problem), :DD (provides information about the step sizes and mode used). Some general explanations are: 1) The algorithm takes steps along what it considers are good directions (using some internal logic), provided that these steps are smaller than what is called the trust-region radius. After a good step (e.g. large energy decrease) it expands the trust-region; after a bad one it reduces it. Sometimes it will try too large a step then have to reduce it, so the energy does not always go down. You can see this by using :DD and :MIN. 2) A grep on :MIN gives a condensed progress output, in which the most significant terms are E (energy in some rescaled units), RELDF (last energy reduction), PRELDF (what the algorithm predicted for the step), RELDX (RMS change in positions in Angstroms) and NPRELDF (predicted change in next cycle). Near the solution RELDF and RELDX should both become small. However, sometimes you can have soft modes in your structure in which case RELDX will take a long time before it becomes small. 3) A warning that the step was reduced due to overlapping spheres if it happens only once (or twice) is not important; the algorithm tested too large a step. However, if it occurs many times it may indicate that the RMT s are too big. 4) A warning CURVATURE CONDITION FAILED indicates that you are still some distance from the minimum, and the Hessian is changing a lot. If you see many of these, it may be that the forces and energy are not consistent. Sometimes PORT gets stuck (often because of inconsistencies of energy and forces due to insufficient scf convergence or a very non-harmonic potential energy surface). A good alternative is NEW1, which is a sophisticated steepest-descent method with optimized step size. It can be very efficient in certain cases, but can also be rather slow when the potential energy surface is rather flat in one, but steep in another direction (eg. a weakly bound molecule on a surface, but constraining the sensitive parameters, like the bond distance of the molecule, may help). Another alternative is NEWT, where one must set proper DELTAs and a FRICTION for each atom. Unfortunately, these DELTAs determine crucially how the minimization performs. Too small values lead to many (unnecessary) geometry steps, while too large DELTAs can even lead to divergence (and finally to a crash). Thus you MUST control how the minimization performs. We recommend the following sequence after 2-3 geometry steps: grep :ENE *mini :ENE : ********** TOTAL ENERGY IN Ry = :ENE : ********** TOTAL ENERGY IN Ry = :ENE : ********** TOTAL ENERGY IN Ry = Good, since the total energy is decreasing. grep :FGL001 *mini :FGL001: 1.ATOM :FGL001: 1.ATOM :FGL001: 1.ATOM

92 74 CHAPTER 5. SHELL SCRIPTS Good, since the force (only a force along z is present here) is decreasing reasonably fast towards zero. You must check this for every atom in your structure. When you detect oszillations or too small changes of the forces during geometry optimization, you will have to decrease/increase the DELTAs in case.inm and rm case.tmpm. (NOTE: You must not continue with modified DELTAs but keeping case.tmpm.) Alternatively, stop the minimization (touch.minstop and wait until the last step has finished), change case.inm and restart. You can get help on its usage with: min -h or min lapw -h PROGRAM: USAGE: min min [OPTIONS] OPTIONS: -j JOB -> job-file JOB (default: run_lapw -I -fc 1. -i 40 ) -noex -> does not extrapolate the density for next geometry step -p -> adds -p (parallel) switch to run_lapw -it -> adds -it (iterative diag.) switch to run_lapw -it1 -> adds -it1 (it.diag. with recreating H_inv) switch to $job -it2 -> adds -it2 (it.diag. with reinitialization) switch to $job -nohinv -> adds -it -nohinv (it.diag. without H_inv) switch to $job -sp -> uses runsp_lapw instead of run_lapw -nohess -> removes.minrestart (initial Hessian) from previous minimization -m -> extract force-input and execute mini (without JOB) and exit -mo -> like -m but without copying of case.tmpm1 to case.tmpm -h/-h -> help -NI -> without initialization of minimization (eg. continue after a crash) -i NUMBER -> max. NUMBER (50) of structure changes -s NUMBER -> save_lapw after NUMBER of structure changes CONTROL FILES:.minstop stop after next structure change For instance for a spin-polarized case, which converges more difficultly, you would use: min -j runsp lapw -I -fc 1.0 -i Phonon calculations Calculations of phonons is based on a program PHONON by K.Parlinski, which runs under MS- Windows and must be ordered separately (see ). Alternatively you may also try the package PHONOPY by Atsushi Togo (see /reg_user/unsupported/). You would define the structure of your compound in PHONON together with a supercell of sufficient size (e.g. 64 atoms). PHONON will then generate a list of necessary displacements of the individual atoms. The resulting file case.d45 must be transfered to UNIX. Here you would run WIEN2k-scf calculations for all displacements and collect the resulting forces, which will be transfered back to PHONON (case.dat and/or case.dsy). With these force information PHONON calculates phonon at arbitrary q-vectors together with several thermodynamic properties init phonon lapw init phonon lapw uses case.d45 from PHONON and creates subdirectories case XX and case XX.struct files for all required displacements. It allows you to define globally RMT values for the different atoms and - initializes every case individually (batch option of init lapw is now supported) or

93 5.5. PARALLEL EXECUTION 75 - initializes every second case (useful for pos. and neg. displacements, which have the same symmetry and thus only one initialization is necessary), or - initializes only the first case and copies the files from the first case to all others. This is most convenient in low symmetry cases with P1 symmetry for all cases and thus just one init lapw needs to be executed (while for higher symmetry a separate initialization is required (but computational effort is reduced). Please use mainly nn to reduce equivalent atoms. sgroup might change the unitcell and than the collection of forces into the original supercell is not possible (or quite difficult). A script run phonon has been created. Modify it according to your needs (parallelization,...) and run all cases to selfconsistency. Note that good force convergence is essential (at least 0.1 mry/bohr) and if your structure has free parameters, either very good equillibrium positions must have been found before, or even better, use both, positive and negative displacements to average out any resulting error from nonequillibrium positions analyse phonon lapw analyse phonon lapw uses the resulting scf files and generates the Hellmann-Feynman -file required by PHONON. When you have positive and negative displacements an automatic averaging will be performed. The resulting case.dat and case.dsy filse should be transfered back to MS-Windows and imported into PHONON. 5.5 Running programs in parallel mode This section describes two methods for running WIEN2k on parallel computers. One method, parallelizing k-points over processors, utilizes c-shell scripts, NFS-file system and passwordless login ((public/private keys). This method works with all standard flavors of Linux without any special requirements. The parallelization is very efficient even on heterogeneous computing environments, e. g. on heterogeneous clusters of workstations, but also on dedicated parallel computers and does NOT need very large network bandwidth. The other parallelization method is based on fine grained methods, MPI and SCALAPACK. It is especially useful for larger systems, if the required memory size is no longer available on a single computer or when more processors than k-points are available. It requires a fast network (Infiniband) or a shared memory machine. Although for small systems (less than 50 atoms/cell) is is not as efficient as the simple k-point parallelization, the current mpi-version has been enhanced a lot and shows for larger problems very good scaling with the number of processors for most parts. In any case, the number of processors and the size of the problem (number of atoms, matrixsize due to the plane wave basis) must be compatible and typically [NMAT / sqrt(processors)].gt should hold. The k-point parallelization can use a dynamic load balancing scheme and is therefore usable also on heterogeneous computing environments like networks of workstations or PCs, even if interactive users contribute to the processors work load. If your case is large enough, but you still have to use a few k-points, a combination of both parallelization methods is possible (always use k-point parallelism first if you have more than 1 k-point) k-point Parallelization Parts of the code are executed in k-parallel, namely lapw1, lapwso, hf, lapw2, lapwdm and optic, qtl, irrep, nmr. These are the numerically intensive parts of most calculations.

94 76 CHAPTER 5. SHELL SCRIPTS Parallelization is achieved on the k-point level by distributing subsets of the k-mesh to different processors and subsequent summation of the results. The implemented strategy can be used both on a multiprocessor architecture and on a heterogeneous (even multiplatform) network. To make use of the k-point parallelization, make sure that your system meets the following requirements: NFS: All files for the calculation must be accessible under the same name and path. Therefore you should set up your NFS mounts in a cluster in such a way, that on all machines the path names are the same. Remote login: ssh to all machines must be possible without specifying a password. This will be handled automatically for a single shared memory machine and when you have specified shared memory during site config (setenv USE REMOTE 0 in $WIENROOT/parallel options). Otherwise you must correctly specify public/private keys for ssh. This can be done by running ssh-keygen -t rsa and copying the id rsa.pub key into /.ssh/authorized keys at the remote sites. The command for launching a remote shell is platform dependent, and usually can be ssh, rsh or remsh. It should be specified during installation when siteconfig lapw is executed (see chapter 11) MPI parallelization Fine grained MPI parallel versions are available for the programs dstart, lapw0, lapw1, lapwso, hf, nmr and lapw2. This parallelization method is based on parallelization libraries, including MPI, ScaLapack, PBlas and FFTW 2 or FFTW 3 (lapw0). The required libraries are not included with WIEN2k. On parallel computers, however, they are usually installed. Otherwise, free versions of these libraries are available 1. The parallelization affects the naming scheme of the executable programs: the fine grained parallel versions of lapw0/1/2/so, dstart and hf are called lapw0 mpi, lapw1[c] mpi, lapwso mpi, dstart mpi, hf[c] mpi, and lapw2[c] mpi. These programs are executed by calls to the local execution environments, as in the sequential case, by the scripts x, dstartpara, lapw0para, lapw1para, lapwsopara, hfpara and lapw2para. On most computers this is done by calling mpirun and this must be configured using siteconfig lapw How to use WIEN2k as a parallel program To start the calculation in parallel, a switch must be set and an input file has to be prepared by the user. The switch -p switches on the parallelization in the scripts x and run lapw. In addition to this switch the file.machines has to be present in the current working directory. In this file the machine names on which the parallel processes should be launched, and their respective relative speeds must be specified. If the.machines file does not exist, or if the -p switch is omitted, the serial versions of the programs are executed. Generation of all necessary files, starting of the processes and summation of the results is done by the appropriate scripts lapw1para, lapwsopara, hfpara, lapwdmpara and lapw2para (when using -p), and parallel programs dstart mpi, lapw0 mpi, lapw1 mpi, lapwso mpi, hf mpi, and lapw2 mpi (when using fine grained parallelization has been selected in the.machines file). org/ 1

95 5.5. PARALLEL EXECUTION The.machines file The following.machines file describes a simple example. We assume to have 5 computers, (alpha,... epsilon), where epsilon has 4, and delta and gamma 2 cpus. In addition, gamma, delta and epsilon are 3 times faster than alpha and beta.: # This is a valid.machines file # granularity:1 1:alpha 1:beta 3:gamma:2 delta epsilon 3:delta:4 epsilon:4 residue:delta:4 lapw0:gamma:2 delta:2 epsilon:4 dstart:gamma:2 delta:2 epsilon:4 To each set of processors, defined by a single line in this file, a certain number of k-points is assigned, which are computed in parallel. In each line the weight (relative speed) and computers are specified in the following form: weight:machine name1:number1 machine name2:number2... where weight is an integer (e.g. a three times more powerful machine should have a three times higher weight). The name of the computer is machine name[1/2/...], and the number of processors to be used on these computers are number[1/2/...]. If there is only one processor on a given computer, the :1 may be omitted. Empty lines are skipped, comment lines start with #. Assuming there are 8 k-points to be distributed in the above example, they are distributed as follows. The computers alpha and beta get 1 each. Two processors of computer gamma and one processor of computers delta and epsilon cooperate in a fine grained parallelization on the solution of 3 k-points, and four processors of computers delta and epsilon cooperate on the solution of 3 k-points. If there were additional k-points, they would be calculated by the first processor (or set of processors) becoming available. With higher numbers of k-points, this method ensures dynamic load balancing. If a processor is busy doing other (e. g., interactive) work, the overall calculation will not stall, but most of its work will be done by other processors (or sets of processors using MPI). This is, however, not an implementation for fail safety: if a process does not terminate (e. g., due to shutdown of a computer) the calculation will never terminate. It is up to the user to handle with such hardware failures by modifying the.machines file and restarting the calculation at the appropriate point. During the run of lapw1para the file.processes is generated. This file is used by lapw2para (and some others) to determine which case.vector* to read. In case you need to create a.processes file for a NEW.machines file and don t want to run lapw1 (for instance in a PBSjob with x lapw1 -p -qtl ) you can issue: x lapw1 -p -d [-up] to create an updated version of this file. A granularity different from 1 (use eg. 3) allows for some load balancing in heterogeneous environments. Suppose you have 10 k-points and 2 nodes, granularity:1 will start 2 jobs with 5 k-points each. However, if node 1 is heavily overloaded, node 2 will idle for quite some time and time will be wasted. With a larger granularity we would decompose the load into 4 or 6 parts. Two jobs would start first, but the next parts go to the node which is free because it has finished earlier. If you can be sure that load balancing is not an issue (eg. because you use a queuing-system and can be sure that you will get 100% of the cpus for your jobs) it is recommended to set granularity:1

96 78 CHAPTER 5. SHELL SCRIPTS for best performance. On shared memory machines it is advisable to add a residue machine to calculate the surplus (residual) k-points (given by the expression MOD(klist, j newweight j) and rely on the operating system s load balancing scheme. Such a residue machine is specified as residue:machine name:number in the.machines file. Alternatively, it is also possible to distribute the remaining k-points one-by-one (and not in one junk) over all processors. The option extrafine:1 can be set in the.machines file. When using iterative diagonalization or the $SCRATCH variable (set to a local directory), the k-point distribution must be fixed. This means, the ratio (k-points / processors) must be integer (sloppy called commensurate at other places in the UG) and granularity:1 should be set. The lines lapw0:gamma:2 delta:2 epsilon:4 dstart:gamma:2 delta:2 epsilon:4 defines the computers used for running lapw0 mpi and dstart mpi. In this example the 8 processors of the computers gamma, delta, and epsilon run lapw0 mpi and dstart mpi in parallel. The parallel dstart is useful for big cases, where core-leakages occured and a core-density superposition is done automatically (activated by the file.lcore) during scf. Please note, parallelization in lapw0 and dstart is done mainly over atoms, thus the number of useful cores is in general different than for lapw1/2/so/hf. If fine grained parallelization is used, each set of processors defined in the.machines file is converted to a single file.machine[1/2/...], which is used in a call to mpirun (or another parallel execution environment). When using a queuing system (like PBS, LoadLeveler or SUN-Gridengine) one can only request the NUMBER of processors, but does not know on which nodes the job will run. Thus a static.machines file is not possible. On can write a simple shell script, which will generate this file on the fly once the job has been started and the nodes are assigned to this job. Examples can be found at our web-site How the list of k-points is split In the setup of the k-point parallel version of LAPW1 the list of k-points in case.klist is split into subsets according to the weights specified in the.machines file: newweight i = weight i klist granularity j weight j where newweight i is the number of k-points to be calculated on processor i. newweight i is always set to a value greater equal one. A loop over all i processors is repeated until all k-points have been processed.

97 5.5. PARALLEL EXECUTION 79 Speedup in a parallel program is intrinsically dependent on the serial or parallel parts of the code according to Amdahl s law: 1 speedup = (1 P ) + P N whereas N is the number of processors and P the percentage of code executed in parallel. In WIEN2k usually only a small part of time is spent in the programs lapw0, lcore and mixer which is very small (negligible) in comparison to the times spent in lapw1 and lapw2. The time for waiting until all parallel lapw1 and lapw2 processes have finished is important too. For a good performance it is therefore necessary to have a good load balancing by estimating properly the speed and availability of the machines used. We encourage the use of testpara lapw or Utils. testpara from w2web to check the k-point distribution over the machines before actually running the programs in parallel. While running lapw1 and lapw2 in parallel mode, the scripts testpara1 lapw (see ) and testpara2 lapw (see ) can be used to monitor the succession of parallel execution Flow chart of the parallel scripts To see how files are handled by the scripts lapw1para and lapw2para refer to figures 5.1 and 5.2. After the lapw2 calculations are completed the densities and the informations from the case.scf2 x files are summarized by sumpara. Note: parallel lapw2 and sumpara take two command line arguments, namely the case.def file but also a number of processor indicator. Figure 5.1: Flow chart of lapw1para On the fine grained parallelization The following parallel programs use different parallelization strategies: dstart mpi is parallelized over the atoms and the K-vectors. This method leads to good scalability as long as there are more atoms than processors. For very many processors, however, the speedup is limited, which is usually not at all critical, since the overall computing time of dstart mpi is quite small. It uses an extra line dstart: in.machines to specify the parallelization.

98 80 CHAPTER 5. SHELL SCRIPTS Figure 5.2: Flow chart of lapw2para lapw0 mpi is parallelized over the number of atoms and with a parallel FFT, which is important in case you have large FFT grids. This method leads to good scalability as long as there are more atoms than processors. For very many processors, however, the speedup is limited, which is usually not at all critical, since the overall computing time of lapw0 mpi is quite small. It uses an extra line lapw0: in.machines to specify the parallelization. lapw1 mpi uses a two-dimensional processor setup to distribute the Hamilton and overlap matrices. For higher numbers of processors two-dimensional communication patterns (4x4=16, 8x8=64,..) are clearly preferable to one-dimensional communication patterns (never use 47 cores, as it gives a 1x47 pattern). Let us assume, for example, 64 processors. In a given processing step, one of these processors has to communicate with the other 63 processors if a one-dimensional setup was chosen. In the case of a two-dimensional processor setup it is usually sufficient to communicate with the processors of the same processor row (7) or the same processor column (7), i. e. with 14 processors. In general the processor array P Q is chosen as follows: P = number of processors, number of processors Q =. Because of SCALAPACK, often P P arrays (i.e. 4, 9, 16,... P processors) give best performance but others are also possible (eg. 2x4=8, 4x8=32,...). Of course it is not recommended to use eg. 17x1 processors. k-point and mpi-parallelization can be used at the same time and are specified by the lines speed:hostname:number of cores in.machines. hf mpi If you use a full hybrid scheme (see also Sect ) and the -hf option for run lapw, then the hf program will be by far the most time consuming part. MPI-parallelization is done over the total number of atoms/cell ( NAT*MULT ) and over the number of occupied bands. Thus it is important that you choose first the best k-parallelization (if you have more than one k-point) and then a MPI-parallelization which is compatible (meaningful) as much as possible with the two parallelizations mentioned above (if you have just 16 occupied bands and 4

99 5.6. CHEMICAL SHIFT NMR CALCULATIONS 81 atoms, for sure using more than 16 cores is completely useless, but probably the scaling will be bad already for more than 4 cores). The parallelization follows that of lapw1 as specified in.machines, although the script uses.processes, which is created at the lapw1 step. lapwso mpi is parallelized over the Hamiltonian. The size is determined by NE*2, where NE is the number of eigenvalues in lapw1 (determined by EMAX in case.in1). Since this size is usually much smaller than the Hamiltonian of lapw1, try to use quadratic processor grids (4x4=16, 8x8=64). Memory size is larger than for the sequential code, but scales with N/4. The parallelization follows that of lapw1 as specified in.machines, although the script uses.processes, which has been created in the lapw1 step. lapw2 mpi is parallelized in two main parts: (i) The density inside the spheres is parallelized over atoms, and (ii) the fast Fourier transforms are done in parallel. In addition the density calculation for each atom can be further parallelized by distributing the eigenvector on a certain subset of processors (usually 2-8). This is in principle not so efficient, but must be used if the memory requirement is too big (typically when lapw2 mpi crashes without reasons) or the network is slow and using more cpu-time but less network traffic is more efficient. Test it out for your hardware and specific case). You set it in.machines using lapw2 vector split:2 Otherwise, the parallelization follows that of lapw1 as specified in.machines, although the script uses.processes, which is created at the lapw1 step. nmr mpi in mode current supports the same parallelization strategy (mixed k-point and mpischeme) as lapw1 or lapw2. The keyword nmr integ: node1 node2... allows for an additional mpi-parallelization (over the atoms) in mode integ (see description in chapter 5.6). If more than one k-point is distributed at once to lapw1 mpi or lapw2 mpi, they will be treated consecutively. Depending on the parallel computer system and the problem size, speedups will vary to some extend. Matrix setup in lapw1 should scale nearly perfect, while diagonalization (using SCALA- PACK) will not. Usually, iterative scales better than full diagonalization and is preferred for large scale computations. Scalability over atoms will be very good if processor and atom numbers are compatible. Running the fine grained parallelization over a 100 Mbit/s or 1,Gbit/s Ethernet network is not recommended, even for large problem sizes. 5.6 Chemical shift NMR calculations Introduction The calculation of the magnetic shielding tensor σ is based on a linear response theory described in Laskowski et al. 2012a,b and In short, the calculation of the NMR shielding tensor requires eigenvectors computed at seven different k-meshes: original and shifted by q in +/- x,y,z direction, where q is small compared to the BZ size. Those eigenvectors are then used to compute the induced current and magnetic susceptibility. The induced current is afterwards integrated (Biot-Savart) to get the NMR shielding tensor. The script x nmr lapw helps you to performs all the necessary steps and together with the NMRprogram (see chapter 8.16) allows you to calculate the chemical shielding (and further the chemical shift with respect to some reference compound). It requieres a converged scf-calculation of your case (and for the time being, the system should be insulating, see below for Knight shifts)

100 82 CHAPTER 5. SHELL SCRIPTS The implemented method uses an enriched APW basis set (extended number of local orbitals, called NMR-LOs). The setup of NMR-LOs is communicated to other programs (for instance lapw1) via the filecase.in1 nmr file (case.in1c nmr for cases without inversion symmetry). Therefore after converging SCF or restoring a previously saved calculation, one has to create case.in1 nmr. The case.in1 nmr file should be generated using: x nmr lapw -mode in1 [parameters] The important parameter here is -nodes val, where val is an integer used to determine the number of NMR-LOs in each orbital quantum number l (see Laskowski,Blaha 2012a, 2014 for details). The default value (8) gives well a converged tensor, but it may also lead to an unnecessarily large basis size. In such cases the number of NMR-LOs may be reduced using a smaller number val (eg. 5), or by using -focus atom option that decreases the number of NMR-LOs for atoms other then the one specified. By default the algorithm implemented here adds NMR-LOs to the bases for all orbital numbers up to l+1, where l is the maximal explicitly specified orbital in case.in1. In a case where the magnetic susceptibility needs to be computed precisely, an l+2 limit may be necessary to reach full convergence. In such cases it is required to add an extra entrance for the next l-value in case.in1 with a default 0.3 linearization energy (eg. a l=2 line for an O atom). You may also consider to run x kgen and create a (finer) k-mesh for the NMR calculation (in any case, the k-point dependency of the NMR tensor should always be tested explicitly by at least 2 different k-meshes. After successful generation of a basic k-mesh and the case.in1 nmr file the NMR shielding tensor can be computed using: x nmr lapw [parameters] By default the x nmr script will execute sequentially the following steps (you don t need to call them explicitly): 1. shifted k-mesh generation based on the existing k-mesh generated previously x nmr lapw -mode klist 2. eigenvectors (lapw1) x nmr lapw -mode lapw1 In a case where spin-orbit coupling needs to be included ( x nmr -so ) the proper eigenvectors vectors are generated with: x nmr lapw -mode lapwso Similarly, for hybrid-dft calculations the eigenvectors will be computed by x nmr lapw -mode hf The eigenvectors are computed sequentially in subdirectories: nmr\_q0 (original k-mesh) nmr\_pqx (shifted in (+q,0,0) in Cartesian frame) nmr\_mqx (shifted in (-q,0,0) in Cartesian frame) nmr\_pqy (shifted in (0,+q,0) in Cartesian frame) nmr\_mqy (shifted in (0,-q,0) in Cartesian frame) nmr\_pqz (shifted in (0,0,+q) in Cartesian frame) nmr\_mqz (shifted in (0,0,-q) in Cartesian frame) If you are using a SCRATCH variable different from./, it is recommended to define a unique scratch directory with x nmr lapw -scratch /scratch/case A

101 5.6. CHEMICAL SHIFT NMR CALCULATIONS 83 in order to avoid collisions between multiple NMR calculations running simultaneously. 3. weight files x nmr lapw -mode lapw2 4. core wave functions x nmr lapw -mode lcore 5. induced current density and magnetic susceptibility x nmr lapw -mode current The current is written to case.current sp (x,y,z), case.current int (x,y,z), where x,y,z are the Cartesian directions of external magnetic field. The current density is UNSYMMETRIZED with respect to irreducible BZ. In order to get a symmetrized current for plotting purposes the full BZ sampling has to be used (x kgen -fbz). The magnetic susceptibility is written to case.xim. 6. integration of current density x nmr lapw -mode integ The full NMR tensor and other related quantities can be found in case.outputnmr integ. The isotropic chemical shift σ iso and its anisotropy is printed under the label :NMR- TOTxxx (in ppm) and :NMRASYxxx (Haeberlen convention): :NMRTOT001 ATOM: Te 1 NMR(total/ppm) Sigma-ISO= Sigma xx= Sigma yy= Sigma zz= :NMRASY001 ATOM: Te 1 NMR(total/ppm) ANISO(delta-sigma)= ASYM(eta) = SPAN= SKEW= The steps 1) to 6) are executed one after another by x nmr script, there is no need to run through them manually. However if there is need to recompute the current without changing eigenvectors (for analysis purposes), steps 5) and 6) can be executed using x nmr lapw -noinit Or when one needs to compute only initialization steps 1) to 4) x nmr lapw -initonly may be used Options All options of the x nmr script can be seen using: x nmr lapw -h -h/h -mode modeid print this message runs in specific mode given by modeid. If mode is not defined, runs sequence needed for actual calculations (klist,lapw1,[lapwso], lapw2, lcore, current, integ), however preceding execution in mode in1 is still required. modeid can be: in1 (initialize case.in1_nmr, adds extra LO) testval (testing case.in1_nmr) klist (initialize shifted k-lists ) lapw1 (executes lapw1) lapwso (executes lapwso, only after lapw1 step)

102 84 CHAPTER 5. SHELL SCRIPTS hf (runs hf on top of lapw1, only after lapw1 step) lapw2 (executes lapw2 for weights, only after lapw1, lapwso or hf) lcore (executes lcore) current (generate induced current) integ (integrates current and computes nmr shielding parameters) plot (plot of the induced current, uses extra input file case.innmrplot, generated automatically if not present) -noinit -initonly -so -orb -hf -hfdir subdir -redklist -diaghf executes mode current and integ executes modes klist, lapw1, [lapwso], lapw2, lcore executes mode lapwso adds LDA+U to lapw1 or lapwso executes mode hf between lapw1 and lapw2 (as this takes long time, you certainly should run this in parallel. If you have more cores, use -hf -hfdir [nmr_q0, nmr_pqx, nmr_mqx...] in parallel) prepares HF vectors (starting from lapw1 and ending with lcore) for the subdir=[q0, pqx, mqx,...]. It allows more parallelization as all "subdir"s can be run with a different.machines file in parallel. uses a reduced k-list (case.klist_rfbz) for the HF potential (note, the general HF k-mesh must be the same as in the scf) diagonal approximation to HF (only eigenvalues updated) -p run in k-point or mpi parallel mode -case name set the casename to name, otherwise the current dir name is used -up include spin polarisation (up spin) -dn include spin polarisation (dn spin) -save dir saves result in directory dir -scratch scratch_dir sets (and creates if necessary) the scratch directory for storing vectors Mode specific parameters (ignored by others): mode: in1 -nodes val number of nodes of the top radial function, default = 8 -focus val index or name of an atom of interest, if not set then all -ovlpmax val maximum allowed overlap between top (energy) radial function from in1 and NMR LO (default 0.6) mode: testval -up/dn include spin polarization (up/dn spin) -orb add LDA+U switch to lapw1 mode: klist -q val sets the q to value, if not defined uses default of mode: lapw1 / lapw2 / lapwso -p run in k-point or mpi parallel mode -up/dn include spin polarization (up/dn spin) -orb add LDA+U switch to lapw1 mode: hf -up/dn include spin polarization (up/dn spin) -hfdir subdir prepares HF vectors (starting from lapw1 up to lcore) for the subdir=[q0, pqx, mqx,...]. It allows additional parallelization as all "subdir"s can be run with a different

103 5.6. CHEMICAL SHIFT NMR CALCULATIONS 85 -redklist -diaghf.machines file in parallel. allows to use a reduced k-list (case.klist_rfbz) for the HF potential (note, the general HF k-mesh must be the same as in the scf) diagonal approximation to HF (only eigenvalues updated) the occupied states OS. Leaves only nonzero alm for iat and l. mode: current -up/dn include spin polarization (up/dn spin) -so use lapwso vectors -hf use hf vectors -emin val overrides the valence bands minimum -emax val overrides the valence bands maximum -iemin val sets lowest valence band to val -iemax val sets highest valence band to val -filt_cxyz_o iat l filter coupling matrix element(<os COUPOP ES>,make_cxyz) the occupied states <OS. Leaves only nonzero alm for iat and l ( FOP_oc>=SUM_es( ES><ES COUPOP OS>/(ENE_os-ENE_es) -filt_cxyz_q iat l filter in coupling matrix elements (<OS COUPOP ES>,make_cxyz) the empty states ES>. Leaves only nonzero alm for iat and l ( FOP_oc>=SUM_es( ES><ES COUPOP OS>/(ENE_os-ENE_es) -filt_curr_o iat l filter in current density (make_current_sp,j(r)=<os JOP FOP>) -filt_curr_fop iat l filter in current density (make_current_sp,j(r)=<os JOP FOP> the perturbation w-f FOP>. Leaves only nonzero alm for iat and l For all -filt_* if (iat.eq. 0) do only interstitial contribution For all -filt_* if (l.lt. 0) apply and sum all l channels -nocc do not add core states to the Green function -noduc do not add du (radial derivative of u) to the Green function -scissor val applies scissor shift to conduction bands -coreonly only core contribution -xionly calculate only macroscopic magnetic suszeptibility -noxi do not calculate macroscopic magnetic suszeptibility -fbz k-sampling uses full BZ (no symmetrization of xi) -scratch dir sets the scratch directory -metal should be set in case of metals, sets default kbt= kbt XX sets kbt for Fermi level smearing in metals for Green function mode: integ -nocore subtract core contribution -up/dn include spin polarization (up/dn spin) mode: plot (note: current is not symmetrized, must use full BZ sampling) -nocore subtract core contribution -up/dn include spin polarization (up/dn spin) Additional notes Parallelization : x nmr lapw -p will execute lapw1, lapw2 and x nmr -mode current -p in k-point parallel mode following the standard WIEN2k scheme. The standard.machines file is used in this case. A mixed k-point/mpi parallelization (if more then one core is assigned to one k-point) is also implemented for x nmr -mode current -p. The integration step x nmr -mode integ

104 86 CHAPTER 5. SHELL SCRIPTS -p supports mpi parallelization over atoms. In order to use it, the following line has to be added to the.machines file: nmr_integ: $proc_list where $proc list is a list of processors. NMR and hybrid DFT : It is possible to combine hybrid-dft and nmr calculations, but note that this is quite expensive, in particular because of additional NMR-local orbital AND the need for ALL eigenvalues, which makes the hf step MUCH more expensive than for a normal scf calculation (and we need calculations for 7 different k-meshes). We therefore recommend a good parallelization (if possible, over ALL k-points and in addition with mpi over the number of atoms/cell). After mode in1 run: x nmr lapw -p -hf or, if you have enough cores create several different.machines files and run the 7 directories in parallel: cp.machine q0.machines x nmr lapw -p -hfdir q0 & cp.machine pqx.machines x nmr lapw -p -hfdir pqx &... Metals : For paramagnetic metals, the Knight shift dominates usually the Chemical shift, which comes from the Fermi-contact term due to the spin-polarization at E F. The contact term can be calculated in an extra directory using a spin-polarized setup. First do a scf cycle using (runsp c lapw -cc (to obtain quickly a non-magnetic solution), then use runsp lapw -orb -cc , where you can apply an external field introducing a spin-polarization (see chapter 7.3). Typically you would apply magnetic fields of T and get the contact term from :HFFxxx. Please note: You need to check carefully the convergence with respect to k-mesh (huge meshes might be necessary). Of course, also the orbital contribution is non-negligible and one should also run x nmr -metal -kbt noxi. Please note: you will usually need an ENOURMOUS k-mesh (more than k-points), and also check convergence with respect to the -kbt 0.00x parameter in the line given above. This procedure excludes the contributions from both, the spin and orbital part of the macroscopic susceptibility, because we have found that this quantity is in most cases still an order of magnitude more difficult to converge. In principle you could run x nmr -noinit -metal -kbt 0.00x -xionly and check the corresponding susceptibility in case.xim. If you can reach convergence, you could add its contribution in the final integration using x nmr -mode integ. Analyses : x nmr lapw -p -noinit -emin xx [-emax yy] allows you to separate the contributions to the magnetic shielding according to the energy range (in Ry) of the valence bands (eg. the contributions from a p-band and a d-band,...). The switch -noinit runs only the modes current and integ. Additional analysis is possible with the -filt options, but requires some understanding of the underlying formalism (see the NMR papers by Laskowski, Blaha). Current plotting : You can also plot the induced current (it needs the dx Dataexplorer software), but since the current is not symmetrized, you need to run first with a full k-mesh. Use x kgen -fbz # for plotting purposes this can be on a smaller k-mesh x nmr lapw x nmr lapw -plot # prepares current.dx and current x/y/z.dx files current2dx lapw

105 5.7. WANNIER FUNCTIONS (WIEN2WANNIER) Wannier functions (wien2wannier) This program was contributed by: Wien2Wannier Version 1.0 by J.Kunes. P.Wisgott and E.Assmann. Please cite the following paper when using it: J.Kunes, R.Arita, P.Wissgott, A.Toschi, H.Ikeda, K.Held, Comp.Phys.Commun. 181, 1888 (2010) Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. wien2wannier is an interface program between WIEN2k and Wannier90 (http://www.wannier.org/) to obtain maximally localized Wannier functions from WIEN2k calculations. It provides the necessary overlap matrices for the construction of Wannier functions and besides some auxilliary programs it also contains a package for plotting the resulting Wannier functions in real space. With this interface, the whole world of Wannier90, i.e. applications which rely on maximally localized Wannier functions and the resulting hopping parameters (Transport, Berry phases (see Chapter 5.8), DMFT) can be combined with WIEN2k. Wannier90 must be installed separately from and should be cited when using it [Mostofi 2008] Usage This section contains only a very brief summary of wien2wannier. Please consult the detailed wien2wannier usersguide for more details, which is available from $WIENROOT/SRC w2w or the textbooks site at For a quick reference, see also the plain-text file CHEATSHEET in $WIENROOT/SRC w2w. Preparatory steps Before running wien2wannier, one needs a converged WIEN2k calculation. Additionally, during the setup for wien2wannier, the bands which are to be taken into account will have to be specified, and the main character (e.g., d bands on atom 2) of these bands should be known. To obtain this information, a combination of partial DOS and bandstructure, or a band character plot is often necessary (e.g. spaghettis fat bands option, or SpaghettiPrimavera and prima.py, available in the unsupported software section of the WIEN2k website). Converge a Wien2k calculation: run[sp sp c] OPTIONS obtain band structure and partial DOS identify target bands and band characters Then create a subdirectory with the necessary files using: prepare w2wdir TARGET which also gets the Fermi energy from case.scf (or case.scf2, if case.scf is not present (take care after x lapw2 -qtl -band!)) and change into this new directory TARGET.

106 88 CHAPTER 5. SHELL SCRIPTS Interface and Wannierization init w2w [-up -dn] generates various input files and performs the following steps: x kgen -fbz Prepares an unshifted k-mesh in the full BZ. Of course, the meshdensity influences the quality of localization of the Wannier functions. x findbands: looks in case.output1 for bands in a given energy range [E min ;E max ] (in ev with EF=0), and outputs the corresponding band indices b min ; b max. To choose the energy window of interest, consult the (partial) DOS and/or a band structure plot. write inwf: prepares the main input file case.inwf for the interface. The band indices b min ; b max have to be specified, and initial projections A mn may be given in terms of atomic sites and appropriate spherical harmonics. write win writes the input file case.win for wannier90.x on the basis of case.inwf and other files. x wannier90 -pp reads the k-mesh in case.win and writes a list of nearest-neighbor k-points to case.nnkp. x lapw1 OPTIONS: computes the eigenvectors on the full-bz k-mesh you may use.machines and -p, -up/-dn, -orb, you may also consider spin-orbit: x lapwso OPTION x w2w [-up -dn] [-p] [-so]: computes the overlaps M nm, initial projections A mn and eigenvalues E n, and writes them to case.mmn, case.amn, and case.eig. x wannier90 [-up -dn] [-so]: computes the U(k) by maximum localization. Output is stored in case.wout. The Wannier orbitals should be converged to a spread which is usually smaller than the unit cell of the structure. Verification and Postprocessing After a successful WANNIER90 run, one should check if the centers and spreads of the Wannier functions (printed in case.wout) are sensible. Another important consistency check is to compare the Wannier-interpolated bandstructure to the one computed by WIEN2k. wien2wannier also provides programs to create a real-space plot of the Wannier functions. compare band structures: With the option hr plot=t in case.win, WANNIER90 writes a bandstructure derived from the Wannier-interpolated Hamiltonian H(k) to case band.dat. To compare this to the bandstructure computed by spaghetti, you can use gnuplot, using the command (including a conversion from Bohr to Å) gnuplot case_band.dat \\ p case.spaghetti_ene u ($4/.53):5, case_band.dat w l The steps for plotting of Wannier functions are: write inwplot: asks for a real-space grid on which the Wannier functions should be plotted, and writes case.inwplot. x wplot -wf m [-up -dn][-p] [-so] evaluates Wannier function number m on the real-space grid, and writes the density w m (r) 2 to case m.psink and the phase argw m (r) to case m.psiarg. use positions from case.wout wplot2xsf converts all case*.psink and case*.psiarg files in the directory to the corresponding xsf files which can be opened by XCrySDen. It can also shift the origin according to case centres.xyz. xcrysden --xsf case m.xsf (or VESTA) visualizes the Wannier functions. Pick Tools - Data Grid from the menu and press OK. In the isosurface controls window choose an appropriate isovalue, e.g. 0.1, and check the Render +/- isovalue box.

107 5.8. SPONTANEOUS POLARIZATION, PIEZOELECTRICITY AND BORN CHARGES (BERRYPI) Help and FAQ Additional information about all programs can be accessed via the help flag, program -h. And of course, read the detailed wien2wannier userguide in $WIENROOT/SRC w2w. In particular there is a FAQ section, which may answer your question. 5.8 Spontaneous Polarization, Piezoelectricity and Born Charges (BerryPI) This program was contributed by: S.J. Ahmed, J. Kivinen, B. Zaporzan, L. Curiel, S. Pichardo, O. Rubel Thunder Bay Regional Research Institute, Ontario, Canada Computer Physics Communications 184, (2013) Sources also available from: https://github.com/spichardo/berrypi Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. These calculations are based on the Modern Theory of Polarization (Berry Phase) pioneered by King-Smith 1993, Resta 1993, which noticed that (in a solid) we can only see a change of polarization P in response to an external perturbation, but not the polarization itself. BerryPI computes both, the ionic and electronic contributions to P using wien2wannier to obtain the overlap integral between two cell periodic parts of the Bloch functions. Of course, this theory applies only to insulators (semiconductors), but not for metals. For more details study the relevant literature (see the CPC paper mentioned above, which should be cited when this module is used in a publication) or the detailed tutorials at $WIENROOT/SRC BerryPI/BerryPI. A current limitation of this implementation is that the structures must have orthogonal lattice vectors. This also means that cubic F and B centered lattices must be converted into a P-type conventional supercell with 4 (2) times as many atoms as the primitive cell. As this should be applied to insulators only, you have to use the TETRA method for the BZ integration. In addition, parallel execution is not yet supported directly (see below) Options The program is called using berrypi -knx:ny:nz [-s -o -j -l] [-h] An online help of all options can be obtained with the -h switch. The parameter -knx:ny:nz is mandatory and determines the k-mesh for the BZ sampling. The additional switches -s allows spin-polarized calculations; -o supports additional orbital potentials (LDA+U or EECE); -j includes spin-orbit coupling (x lapwso); and -l skips the lapw1 run. The option -l can be used to make the most time consuming lapw1 step running in parallel. Execute x kgen -fbz ; x lapw1 -p and join vectorfiles case NUM before the call fo berrypi -l.

108 90 CHAPTER 5. SHELL SCRIPTS Spontaneous Polarization To obtain P one has to do two calculations, one for the unperturbed structure (λ 0 ) and one for the perturbed one (λ 1 ) and obtain P=P 1 -P 0. Start out with the distorted structure (eg. the ferroelectric phase of BaTiO 3 ) and perform a standard WIEN2k calculation. Then run the berrypi program: mkdir case;cd case;mkdir case0;mkdir case1 # create suitable directories cd case1 makestruct # create your structure init_lapw -b... # initialize wien2k run_lapw... # run scf cycle berrypi -k6:6:6 # run berrypi where -k defines a suitable k-mesh. This will give you the corresponding x,y,z components of the polarization as: ========================================================================= Value spin dir(1) dir(2) dir(3) Electronic polarization (C/m2) sp(1) [ e-12, e-13, e-01] Ionic polarization (C/m2) sp(1) [ e-11, e-11, e-01] Tot.spin polariz.=pion+pel(c/m2) sp(1) [ e-12, e-11, e-01] TOTAL POLARIZATION (C/m2) both [ e-12, e-11, e-01] ========================================================================== Now copy all files to the case0 directory, rename the files and change the struct file such that it corresponds to the undistorted (cubic) structure (keeping all other inputs identical: cd..;cp -r case1 case0;cd case0;rename_files case1 case0 edit case0.struct # create undistorted structure x dstart # new starting density run_lapw... # run scf cycle berrypi -k6:6:6 # run berrypi The spontaneous polarization in z-direction is defined as the difference in z component of polarization between the non-centrosymmetric P z (λ 1 ) and centrosymmetric structure P z (λ 0 ). In this case P z (λ 0 ) = 0 (output not shown) and the resultant spontaneous polarization is P s =0.31 C/m 2. Please consider the effects of possible π wrapping, so in general the smallest possible value should be considered. If there is a suspect of π-wrapping artifacts, it is useful to study intermediate structures (between λ 1 and λ 0 ) and ensure continuity in the evolution of P z Born effective charges The Born effective charge Zs,αβ of an atom s is defined as the change in polarization due to a displacement of its position. These charges are also used to estimate the LO/TO splitting of the optical vibrational modes at Γ. For the calculation of the Born effective charge of As in GaAs one has first to create a P -type supercell with 4 formula units/cell (see limitations above). One of the 4 As atoms has to be displaced along the z-axis from it s equilibrium position by +0.01(λ 1 ) and -0.01(λ 2 ) in fractional coordinates. Then perform (identical) WIEN2k calculations for the two structures and run berrypi -k6:6:6. The two calculations yield lines like:

109 5.8. SPONTANEOUS POLARIZATION, PIEZOELECTRICITY AND BORN CHARGES (BERRYPI)91 "lambda1" ELECTRONIC POLARIZATION ========================================================================= Value spin dir(1) dir(2) dir(3) Berry phase (rad) [-pi... +pi] up+dn [ e-10, e-09, e+00] Electronic polarization (C/m2) sp(1) [ e-11, e-10, e-02] ========================================================================= IONIC POLARIZATION ========================================================================= Elem. Fractional coord. spin val dir(1) dir(2) dir(3) Total ionic phase wrap. (rad) sp(1) [ e-09, e-09, e-01] Ionic polarization (C/m2) sp(1) [ e-10, e-10, e-02] ========================================================================== "lambda2" ELECTRONIC POLARIZATION ========================================================================== Value spin dir(1) dir(2) dir(3) Berry phase (rad) [-pi... +pi] up+dn [ e-10, e-09, e+00] Electronic polarization (C/m2) sp(1) [ e-11, e-10, e-02] ========================================================================== IONIC POLARIZATION ========================================================================== Elem. Fractional coord. spin val dir(1) dir(2) dir(3) Total ionic phase wrap. (rad) sp(1) [ e-09, e-09, e-01] Ionic polarization (C/m2) sp(1) [ e-10, e-10, e-02] ========================================================================== The total (ionic + electronic) phase along z-axis in the case of λ 1 and λ 2 is and rad, respectively. The Born charge can be obtained from these phases φ as Z zz = π 2 δφ z δρ z (5.1) where δρ is the relative displacement (0.02) in fractional coordinates. The calculation yields Z zz = The negative sign is indicative of a higher electronegativity of As as compared to that for Ga. Please consider the effects of possible π wrapping, so in general the smallest possible value should be considered Piezoelectric constants For such calculations you need to calculate the Berry phases for the reference (equillibrium) structure (e.g. the tetragonal ferroelectric PbTiO 3 structure) and a perturbed structure, where a compressive strain ɛ z of 0.1 % has been applied in the z-direction (for the latter structure one should also perform a new optimization of the internal coordinates).

110 92 CHAPTER 5. SHELL SCRIPTS The piezoelectric coefficient ε zz is defined as change in polarization with respect to the applied strain: ɛ zz = dp z dɛ z (5.2) 5.9 Getting on-line help As mentioned before, all WIEN2k csh-shell scripts have a help -switch -h, which gives a brief summary of all options for the respective script. To obtain online help on input-parameters, program description,... use help lapw which opens the pdf-version of the users guide (using acroread or what is defined in $PDF- READER). You can search for a specific keyword using f keyword. This procedure substitutes an Index and should make it possible to find a specific information without reading through the complete users guide. In addition there is a html-version of the UG and its starting page is: $WIENROOT/SRC usersguide html/usersguide.html When using the user interface w2web, you have access to the html and pdf-version (the latter requires an X-windows environment) of the usersguide. At our webserver we put informations for the registered user: A FAQ page with answers to some common problems. Update information: When you think the program has an error, please check wether newer versions are available, which might have fixed the problem you encounter. A mailing list: Please check the digest! In many cases your questions may have been answered before. Locate your problem: If a calculation crashes, please locate the problem. Check the content of files like case.dayfile, *.error, case.scf, case.scfx, case.outputx where X specifies the program which crashed. Posting questions: Please provide enough information so that somebody can help you. A question like: My calculation crashed. Please help me! will most likely not be answered Interface scripts We have included a few interface scripts into the current WIEN2k distribution, to simplify the previewing of results. In order to use these scripts the public domain program gnuplot has to be installed on your system eplot lapw The script eplot lapw plots total energy vs. volume or total energy vs. c/a-ratio or b/a-ratio using the file case.analysis. The latter should have been created with grepline (using :VOL and :ENE labels) or the Analysis Analyze multiple SCF-files menu of w2web and the file names must be generated (or compatible) with optimize.job. Alternatively you can use eplot lapw -a search-string-in-scf-files, which generates case.analysis automatically using the specified string. For a description of how to use the script for batch like execution call the script using

111 5.10. INTERFACE SCRIPTS 93 eplot lapw -h gibbs lapw The script gibbs lapw (provided by M. Jamal) is an extension of eplot lapw and can also plot Volume vs. Pressure curves as well as the Gibbs energy difference (stored in case.outputdeltag) of two different phases as function of Pressure. When interested in pressure driven phase transitions, one can do calculations for the two phases of interest in two different subdirectories and perform Volume optimization (using x optimize; optimize.job, see sec. 5.3). Once this has been finished, one can use gibbs lapw (instead of eplot lapw), which will also create case.outputeos meshp, eos.meshp1 and deos1 files. These files allow for a comparison of the Gibbs energy as function of pressure for the two different phases. A typical sequence to determine the transition pressure of this phase transition (assuming that the struct files and initializations have been done before) would look like: cd dir1 x optimize # select Volume optimization and a suitable volume range optimize.job # eventually change some run or save-options before gibbs lapw -v vol cd../dir2 x optimize # select Volume optimization and a suitable volume range optimize.job # eventually change some run or save-options before cp../dir1/eos.meshp1 eos.meshp2 cp../dir1/deos1 deos2 gibbs lapw -v vol For a description of how to use the script for batch like execution call the script using gibbs lapw -h which will yield: gibbs lapw [-v vol] [-a string in scf-files] [-plt/-gbs/-ene] For instance, gibbs lapw -a pbe will analyse all scf files *pbe.scf parabolfit lapw The script parabolfit lapw is an interface for a harmonic fitting of E vs. 2-4-dim lattice parameters by a non-linear least squares fit (eosfit6) using PORT routines. Once you have several scf calculations at different lattice parameters (usually generated with optimize.job) it generates the required case.ene and case.latparam from your scf files. Using parabolfit lapw [ -t 2/3/4 ] [ -f FILEHEAD ] [ -scf *xxx*.scf ] you can optionally specify the dimensionality of the fit or the specific scf-filenames.

112 94 CHAPTER 5. SHELL SCRIPTS dosplot lapw The script dosplot lapw plots total or partial Density of States depending on the input used by case.int and the interactive input. It can be used to generate all partial DOS plots in a simple way to get an overview. A more advanced plotting interface is provided by dosplot2 lapw, see below. For a description of how to use the script for batch like execution call the script using dosplot lapw -h dosplot2 lapw The script dosplot2 lapw plots total or partial Density of States depending on the input used by case.int and the interactive input. It can plot up to 4 DOS curves into one plot, and simultaneously plot spin-up/dn DOS. It supports also the SUM-DOS option (see description of TETRA. It was provided by Morteza Jamal (m modified by PB. For a description of how to use the script for batch like execution call the script using dosplot2 lapw -h You can also use the script dosplot all lapw [-up] to generate default-plots (4 lines per plot) of all partial DOS cases as defined in case.int Curve lapw The script Curve lapw plots x,y data from a file specified interactively. It asks for additional interactive input. It can plot up to 4 curves into one plot and is a simple gnuplot interface. It was provided by Morteza Jamal (m specplot lapw specplot lapw provides an interface for plotting X-ray spectra from the output of the xspec or txspec program. For a description of how to use the script for batch like execution call the script using specplot lapw -h rhoplot lapw The script rhoplot lapw produces a surface plot of the electron density from the file case.rho created by lapw5. Note: To use this script you must have installed the C-program reformat supplied in SRC reformat.

113 5.10. INTERFACE SCRIPTS prepare xsf lapw This program was contributed by: David Koller Institute for MaterialsChemistry TU Vienna Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. The script prepare xsf lapw produces 3D data of the electron density (or the potential) in XCrysDen-format (case.xsf) for plotting with XCrysDen (Menu Tools Data Grid). It is written in Python and also uses the programs lapw5 and str2xcr.exe (included in the WIEN2k distribution). It requires an input file case.inxsf: # This is an inxsf-file >D9 clmval # unit # 9 in def-file >D1 clmvaldn # unit # 11 in def File >IS # Start of end part of in5-file RHO ATU VAL NODEBUG # careful VAL/TOT!!! NONORTHO >IE # closes what was started with >IS >C # Start-Corner of part of unit cell (compared to lattice vectors of conventional cell) >CX # x-end >CY # y-end >CZ # z-end # use for fcc: #>C #>CX #>CY #>CZ # entire cell: #>C #>CX #>CY #>CZ >NX 30 # number of data points in x-direction >NY 30 >NZ 30 >IZ # additional cells in in5-file >PS # parallel start machine1 machine1 machine2 >PE # parallel end # >PM # End of inxsf-file In this file comments are designated by #. Markers at the beginning of a line consisting of > followed by two characters determine the content of this line or of the following lines, depending on the marker. Explanation of the markers: >D9: The suffix of the main data file. It corresponds to unit 9 in the file lapw5.def

114 96 CHAPTER 5. SHELL SCRIPTS >D1: The suffix of a second data file which can be optionally added to or subtracted from the main data file. It corresponds to unit 11 in the file lapw5.def >IS: This starts a section which needs to be closed with >IE. The lines between these two markers will be used as lines 6-8 in the in5-file. >IZ: This will be used as line 4 in the in5-file. >C0: Coordinates of a corner of a three-dimensional box, delimited by parallel planes, in which the data should be plotted. The units of these numbers are the unit vectors of the conventional cell (e.g is the centre of the xy-plane which would be the 1d-position in space group 111) >CX: Coordinates of the x-end corner of the box >CY: Coordinates of the y-end corner of the box >CZ: Coordinates of the z-end corner of the box >NX: Number of data points in x-direction >NY: Number of data points in y-direction >NZ: Number of data points in z-direction >PS / >PE / >PM: determine the parallelization This script also contains support for parallel execution. One possibility is to include >PM. In this case the file.machines is used to determine which hosts are used. More details can be found in the section about parallel WIEN2k. If >PM is not present (or commented) it is possible to specify the desired hosts between >PS and >PE. If neither >PM nor >PS are present, the script will be executed in non-parallel way which should work well enough in most cases opticplot lapw The script opticplot lapw produces XY plots from the output files of the optics package using the case.joint, case.epsilon, case.eloss, case.sumrules or case.sigmak. For a description of how to use the script for batch like execution call the script using opticplot lapw -h addjoint-updn lapw The script addjoint-updn lapw adds the files case.jointup and case.jointdn together and produces case.joint. It uses internally the program add columns. It should be called for spin-polarized optics calculations after x joint -up and x joint -dn, because the Kramers- Kronig transformation to the real part of the dielectric function (ɛ 1 ) is not a simple additive quantity concerning the spin (see Ambrosch-Draxl 06). The KK transformation should then be done non-spinpolarized (x kram) resulting in files: case.epsilon, case.eloss, case.sumrules or case.sigmak. This script can also be missused to add or subtract (add the keyword sub ) the content of case.jointup and case.jointdn, when they come from calculations of different band-ranges,...

115 6 Programs for the initialization Contents 6.1 NN SGROUP SYMMETRY LSTART KGEN DSTART In sections ( ) we describe the initial utility programs. These programs are used to set up a calculation. 6.1 NN (nearest neighbor distances) This program uses the case.struct file (see 4.3) in which the atomic positions in the unit cell are specified, calculates the nearest neighbor distances of all atoms, and checks that the corresponding atomic spheres (radii) are not overlapping. If an overlap occurs, an error message is shown on the screen. In addition, the next nearest-neighbor distances up to f times the nearest-neighbor distance (f must be specified interactively) are written to an output file named case.outputnn. For negative f values only the distances of non-equivalent atoms are printed., but equivalent ones are not listed again. Optionally one can specify also a dlimit parameter, which helps nn to find equivalent atoms in case of inaccuarate structural data. It is highly recommended in most cases that you change your sphere sizes and do NOT use the default of 2.0. An increase from 2.0 to 2.1 may already result in drastically reduced computing time. More recommendations are given in chapter 4.3. nn also checks if equivalent atoms are specified correctly in case.struct. At the bottom of case.outputnn the coordination shell-structure is listed and from that a comparison with the input is made verifying that equivalent atoms really have equivalent environments. If this is not the case, an ERROR will be printed and a new structure file case.struct nn is generated. You have to recheck your input and then decide whether you want to accept the new structure file, or reject it (because the equivalency may just be an artefact due to a special choice of lattice parameters). It also may be that you have made a simple input error. If you want to force two atoms of the same kind (e.g. 2 Fe atoms) to be nonequivalent (e.g. because you want to do an antiferromagnetic calculation), label the atoms as Fe1 and Fe2 in case.struct. Thus this program helps to generate proper struct-files especially in the case of artificial unit cells, e.g. a supercell simulating an impurity or a surface. It also prints the bond-valences (see also the comments in $WIENROOT/SRC nn/bva). 97

116 98 CHAPTER 6. INITIALIZATION Execution The program nn is executed by invoking the command: nn nn.def or x nn 6.2 SGROUP This program was contributed by: Bogdan Yanchitsky and Andrei Timoshevskii Institute of Magnetism, Kiev, Ukraine and Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. It was published in Yanchitsky and Timoshevskii 2001, and is written in C. This program uses information from case.struct (lattice type, lattice constants, atomic positions) and determines the spacegroup as well as all pointgroups of non-equivalent sites. It uses the nuclear charges Z or the label in the 3rd place of the atomic name (Si1, Si2) to distinguish different atoms uniquely. It is able to find possible smaller unit cells, shift the origin of the cell and can even produce a new struct file case.struct sgroup based on your input case.struct with proper lattice types and equivalency. It is thus most useful in particular for handmade structures. For more information see also the README in SRC sgroup Execution The program sgroup is executed by invoking the command: sgroup -wi case.struct [-wo case.struct sgroup] case.outputsgen or x sgroup 6.3 SYMMETRY This program uses information from case.struct (lattice type, atomic positions). If NSYM was set to zero it generates the space group symmetry operations and writes them to case.struct st to complete this file. Otherwise (NSYM > 0) it compares the generated symmetry operations with the already present ones. If they disagree a warning is given in the output. In addition the point group of each atomic site is determined and the respective symmetry operations and LM values of the lattice harmonics representation are printed. The latter information is written into case.in2 sy, while the local rotation matrix, the positive or negative IATNR values and the proper ISPLIT parameter are written to case.struct st. (See appendix A and Sec. 4.3).

117 6.4. LSTART Execution The program symmetry is executed by invoking the command: symmetry symmetry.def or x symmetry 6.4 LSTART (atomic LSDA program) lstart is a relativistic atomic LSDA code originally written by Desclaux (69, 75) and modified for the present purpose. Internally it uses Hartree atomic units, but all output has been converted to Rydberg units. lstart generates atomic densities which are used by dstart to generate a starting density for a scf calculation and all the input files for the scf run: in0, in1, in2, inc and inm (according to the atomic eigenvalues). In addition it creates atomic potentials (which are truncated at their corresponding atomic radii and could be used to run lapw1) and optional atomic valence densities, which can be used in lapw5 for a difference density plot. The atomic total energies are also printed, but it can only be used for cohesive energy calculations of light elements. Already for second-row elements the different treatment of relativistic effects in lstart and lapwso yields inconsistent data and you must calculate the atomic total energy consistently by a supercell approach via a bandstructure calculation (Put a single atom in a sufficiently large fcc-type unit cell). If the program stops with some lines: NSTOP=... in case.outputst, this means, that a proper solution for at least one orbital could not be obtained. In such a case the input must be changed and one should provide different occupation numbers for these states (e.g. Cu can not be started with 3d 10 4s 1, but it works with 3d 9 4s 2 ). The program produces WARNINGS if R0 is too big or core-density leaks out of RMT Execution The program lstart is executed by invoking the command: lstart lstart.def or x lstart [-sigma] The files case.rsp(up dn) are generated and contain the atomic (spin) densities, which will be used by DSTART later on. Using -sigma generates case.inst sigma with modified input to generate case.sigma used for difference densities (see below) Dimensioning parameters The following parameters are defined in file param.inc (static and not allocatable arrays): NPT total number of radial mesh points, must be gt.(nrad+npt00), where NRAD is the number of mesh-points up to RMT specfied in case.struct. NPT00 max. number of radial mesh points beyond RMT RMAX0 max. distance of radial mesh

118 100 CHAPTER 6. INITIALIZATION Input When running lstart you will first be asked interactively to specify an XC-potential switch. Currently 5 (LSDA, Perdew and Wang 92) as well as 11, 13 and 19 (three GGAs, Wu,Cohen 06; the standard PBE Perdew et al. 96, as well as PBEsol, Perdew et al. 08; respectively) are officially supported, 13 is the standard PBE-GGA. In addition the program asks for an energy cut-off, separating core from valence states. Usually -6.0 Ry is a good choice, but you should check for each atom how much core charge leaks out of the sphere (WARNINGS in case.outputs). If this is the case one should lower this energy cut-off and thus include these low lying states into the valence region. Alternatively you can also select a charge localization criterium (usually between 0.97 and ). This allows a more localized state (like a 4f of 5d elements) to be core, while a more delocalized state at lower energy (like the 5p states of 5d elements) to be semi-core. The rest of the input is described in the sample input below. Note: Only the data at the beginning of the line are read whereas the comment describes the respective orbitals. This file can be generated automatically in w2web during Initialize calc. or using SinglePrograms instgen lapw or with the script instgen lapw. To edit this file by hand choose View/Edit Input Files and choose case.inst top of file: case.inst ZINC Ne 6 (inert gas, # OF VALENCE ORBITALS not counting spin) 3,-1,1.0 N ( N,KAPPA,OCCUP; = 3S UP, 1 ELECTRON) 3,-1,1.0 N 3S DN 3,-2,2.0 N 3P UP 3,-2,2.0 N 3P DN 3, 1,1.0 N 3P*UP 3, 1,1.0 N 3P*DN 3,-3,3.0 P 3D UP 3,-3,3.0 P 3D DN 3, 2,2.0 P 3D*UP 3, 2,2.0 P 3D*DN 4,-1,1.0 P 4S UP 4,-1,1.0 P 4S DN **** END OF Input **** END OF Input bottom of file Interpretive comments follow: line 1: format(a4,a6) title, keyword title keyword The keyword Watson enables a stabilization of negative ions using a Watson -sphere of radius R-wat with charge Q-wat, which must be given in the next line when this keyword is specified. The keyword PRATT enables a scf mixing using standard PRATT scheme. It might be useful if a certain atomic configuration does not converge with the standard mixing scheme and requires a (usually quite small) mixing factor, which must be given in the next line when this keyword is specified. line 2: free format config

119 6.5. KGEN 101 config specifies the core state configuration by an inert gas (He, Ne, Ar, Kr, Xe, Rn) and the number of (valence) orbitals (without spin). (In the example given above one could also use Ar 3 and omit the 3s and 3p states.) The atomic configurations are listed in the appendix and can also be found online using periodic table, a shell script which displays SRC/periodic.ps with ghostview) line 3: format(i1,1x,i2,1x,f5.3,a1) n, kappa, occup, plot n kappa occup plot the principle quantum number the relativistic quantum number (see below) occupation number (per spin) P specifies that the density of the respective orbital is written to the file case.sigma, which can be used for difference density plots in lapw5. N or an empty field will exempt density of the respective orbital from being printed to file. >>>:line 3 is repeated for the other spin and for all orbitals specified above by config. >>>: the last two lines must be **** **** optional inserted as line 2 when Watson has been specified in line 1: free format R-wat, Q-wat R-wat radius of a charged sphere used to stabilize otherwise unstable negative ions (e.g. 2.5 for O 2 ) Q-wat charge of the stabilizing sphere, (e.g. 2 for O 2 ) The quantum numbers are defined as follows (see e.g. Liberman et al 65): Spin quantum number: s = +1 or s = 1 Orbital quantum number j = l + s/2 Relativistic quantum number κ = s(j + 1/2) j = l + s/2 κ max. occupation l s = 1 s = +1 s = 1 s = +1 s = 1 s = +1 s 0 1/2-1 2 p 1 1/2 3/ d 2 3/2 5/ f 3 5/2 7/ Table 6.6: Relativistic quantum numbers 6.5 KGEN (generates k mesh) This program generates the k-mesh in the irreducible wedge of the Brillouin zone (IBZ) on a special point grid, which can be used in a modified tetrahedron integration scheme (Blöchl et al 1994). kgen needs as interactive input the total number of k-points in the BZ. If this is set to zero, you are asked to specify the divisions of the reciprocal unit-cell vectors (3 numbers, be careful not to break symmetry and choose them properly according to the inverse lenght of the reciprocal

120 102 CHAPTER 6. INITIALIZATION lattice vectors) for a mesh yourself. If inversion symmetry is not present, it will be added automatically unless you specified the -so switch (for magnetic cases with spin-orbit coupling). The k-mesh is then created with this additional symmetry. If symmetry permits, it further asks whether or not the k-mesh should be shifted away from high symmetry directions. The file case.klist is used in lapw1 and case.kgen is used in tetra and lapw2, if the EF switch is set to TETRA, i.e. the tetrahedron method for the k-space integration is used. For the format of the case.klist see page Execution The program kgen is executed by invoking the command: kgen kgen.def or x kgen [-so -fbz -hf] With the switch -so it uses a file case.ksym (usually generated by symmetso) instead of case.struct and does not add inversion symmetry. The -fbz switch generates a k-mesh in the full Brillouinzone (no symmetry) Dimensioning parameters The following parameters are used in main.f, ord1.f (static arrays): IDKP NWX INDEXM number of inequivalent k-points (like NKPT in other programs) internal parameter, must be increased for very large k-meshes internal parameter, must be increased for very large k-meshes 6.6 DSTART (superposition of atomic densities) This program generates an initial crystalline charge density case.clmsum by a superposition of atomic densities (case.rsp) generated with lstart. Information about LM values of the lattice harmonics representation and number of Fourier coefficients of the interstitial charge density are taken from case.in1 and case.in2. In the case of a spin-polarized calculation it must also be run for the spin-up charge density case.clmup and spin-down charge density case.clmdn Execution The program dstart is executed by invoking the command: dstart dstart.def or x dstart [-up dn -c -fft -super -lcore -p] With the switch -fft dstart will terminate after case.in0 std has been created. The switch -super will produce new super.clmsum instead of case.clmsum, which is necessary for charge extrapolation (clmextrapol lapw). -lcore produces case.clmsc from the radial core densities case.rsplcore (this is activated during scf when a.lcore file is present. It can run in mpi-parallel mode (-p) for big cases (typically more than 20 atoms) and core-superposition Dimensioning parameters The following parameters are collected in file module.f, but usually need not to be changed:

121 6.6. DSTART 103 NPT LMAX2 NCOM number of r-mesh points in atomic density (should be the same as in LSTART) max l in LM expansion number of LM terms in density

122 104 CHAPTER 6. INITIALIZATION

123 7 Programs for running an SCF cycle Contents 7.1 LAPW DFTD ORB HF LAPW LAPWSO LAPW SUMPARA LAPWDM LCORE MIXER In sections we describe the main programs to run an SCF cycle as illustrated in figure LAPW0 (generates potential) lapw0 computes the total potential V tot as the sum of the Coulomb V c and the exchange-correlation potential V xc using the total electron (spin) density as input. It generates the spherical part (l=0) as case.vsp and the non-spherical part as case.vns. For spin-polarized systems, the spindensities case.clmup and case.clmdn lead to two pairs of potential files. These files are called: case.vspup, case.vnsup and case.vspdn, case.vnsdn. The Coulomb potential is calculated by the multipolar Fourier expansion introduced by Weinert (81). Utilizing the spatial partitioning of the unit cell and the dual representation of the charge density [equ. 2.10], firstly the multipole moments inside the spheres are calculated (Q-sp). The Fourier series of the charge density in the interstitial also represent SOME density inside the spheres, but certainly NOT the correct density there. Nevertheless, the multipole moments of this artificial plane-wave density inside each sphere are also calculated (Q-pw). By subtracting Q-pw from Q-sp one obtains pseudo-multipole moments Q. Next a new plane-wave series is generated which has two properties, namely zero density in the interstitial region and a charge distribution inside the spheres that reproduces the pseudo-multipole moments Q. This series is added to the original interstitial Fourier series for the density to form a new series which has two desirable properties: it simultaneously represents the interstitial charge density AND it has the same multipole moments inside the spheres as the actual density. Using this Fourier series the interstitial Coulomb potential follows immediately by dividing the Fourier coefficients by K 2 (up to a constant). Inside the spheres the Coulomb potential is obtained by a straightforward classical Green s function method for the solution of the boundary value problem. 105

124 106 CHAPTER 7. SCF CYCLE The exchange-correlation potential is computed numerically on a grid. Inside the atomic spheres a Gauss-Legendre integration is used to reproduce the potential using a lattice harmonics representation. In the interstitial region a 3-dimensional fast Fourier transformation (FFT) is used. The total potential V is obtained by summation of the Coulomb V C and exchange-correlation potentials V xc. In order to find the contribution from the plane wave representation to the Hamilton matrix elements we reanalyze the Fourier series in such a way that the new series represents a potential which is zero inside the spheres but keeps the original value in the interstitial region and this series is put into case.vns. The contribution to the total energy which involves integrals of the form ρ V is calculated according to the formalism of Weinert et al (82). The Hellmann-Feynman force contribution to the total force is also calculated (Yu et al 91). Finally, the electric field gradient (EFG) is calculated in case you have an L=2 term in the density expansion. The EFG tensor is given in both, the local-rotation-matrix coordinate system, and then diagonalized. The resulting eigenvectors of this rotation are given by columns. For surface calculations the total and electrostatic potential at z=0 and z=0.5 is calculated and can be used as energy-zero for the determination of the workfunction. (It is assumed that the middle of your vacuum region is either at z=0 or z=0.5) Execution The program lapw0 is executed by invoking the command: lapw0 lapw0.def or x lapw0 [ -p -eece -grr] Dimensioning parameters The following parameters are used (they are collected in file param.inc, but usually need not to be changed: NCOM number of lm components in charge density and potential representation; it must satisfy the following condition: NCOM+3.gt. {[number of l, m with m = 0] + [2 * number of l, m with m > 0]} NRAD number of radial mesh points LMAX2 highest L in the LM expansion of charge and potential LMAX2X highest L for the gpoint-grid in the xcpot generation (may need large values for -eece ) restrict output for mpi-jobs, limits the number of case.output0xxx files to restrict output Input The input is very simple. It is generated automatically by init lapw, and needs to be changed only if a different exchange-correlation potential should be used: top of file: case.in TOT XC_PBE! MULT/COUL/EXCH/POT /TOT ; VXC-SWITCH NR2V IFFT 8! R2V EECE/HYBR IFFT LUSE ! min IFFT-parameters, enhancement factor, iprint (#of FK in E-field expansion, EFELD (Ry) bottom of file

125 7.1. LAPW0 107 Interpretive comments follow: line 1: free format switch, indxc, xc1 switch indxc TOT total energy contributions and total potential calculated KXC total energy contributions and total potential calculated. In addition the kinetic energy contribution as well as the XC-energy will be printed. POT total potential is calculated, but not the total energy MULT multipole moments calculated only COUL Coulomb potential calculated only EXCH exchange correlation potential calculated only NOTE: MULT, COUL, and EXCH are for testing only, whereas POT, saves some CPU time if total energy is not needed keyword(s) to specify type of exchange and correlation potential. The most common options are listed below (for all options see Table 7.3 below), the description in sections about full-hybrid functionals (4.5.8) or Onsite-exact-exchange for correlated electrons (4.5.7) or the SRC lapw0/vxclm2.f subroutine): XC LDA Perdew and Wang 92, parameterization of Ceperly-Alder data, the recommended LDA option (former option 5) XC PBE Generalized Gradient approximation PBE by Perdew-Burke-Ernzerhof 96 (former option 13) XC WC Generalized Gradient approximation (Wu-Cohen 2006, Tran et al. 2007)(former option 11) XC PBESOL Generalized Gradient approximation (PBEsol, Perdew 2008) (former option 19) XC MGGA MS probably best Meta-GGA (energy functional only, uses PBE for the potential) up to now (Sun et al. 2013). In order to generate the requiered case.vresp* files, you need case.inm vresp (cp $WIENROOT/SRC templates/template.inm vresp case.inm vresp and run one scf cycle with XC PBE after creation of case.inm vresp. Only afterwards change indxc to XC MGGA MS. In addition you must use very large IFFT parameters, otherwise it might be numerically unstable. XC REVTPSS Meta-GGA RevTPSS (Perdew et al. 2009). (V XC of PBESOL, see also the notes in previous option above.) (former option 29) XC MBJ modified Becke-Johnson (mbj-lda) potential V XC (Tran and Blaha 2009). Uses the mbj-exchange + LDA-correlation potential and yields gaps in very good agreement with experiment. The xc-energy E XC is from LDA. For detailed usage see chapter about mbj calculations (4.5.9). EX SWITCH EC SWITCH VX SWITCH VC SWITCH (up to) four keywords for XC-energies and potentials, where SWITCH has to be replaced by some keyword:

126 108 CHAPTER 7. SCF CYCLE xc1 NONE, LDA, PBE, WC (EX,VX), PBESOL, PKZB (EX,EC meta-gga of Perdew 1999), PW91, EV93 (EX,VX, Engel-Vosko 1993), RPBE (EX,VX), B88 (EX,VX), AM05, SOGGA (EX,VX), MPBE, LYP (EC,VC), TPSS (EX,XC), REVTPSS (EX,EC), S (VX, reduced density gradient s, for plotting only), RS (VX, r s value for plotting only), LAPRHO (VX, 2 ρ for plotting only), TAU-TAUW (VX, kinetic energy density difference for plotting only), TAU (VX, kinetic energy density for plotting only), Z (VX, inhomogeneity measure for plotting only), VSXC (EX,EC), AK13 (EX,VX), HTBS (EX,VX, see Haas 2011), GRR (EX,VX, average of ρ/ρ), and screened-hybrid-dft options for VX,EX (SLDA, SPBE, SWC, SPBESOL, SB88). (see also Table 7.3 below) optional inputs for certain XC options: XC MGGA MS: xc1 = XC LDA or XC PBE: to modify the spin scaling (reduction of spinpolarization) according to (Ortenzi et al. 2012). xc1 must be between 0 and 2. OPTION EX SWITCH EC SWITCH VX SWITCH VC SWITCH VRESP GGA AEQ XC LDA EX LDA EC LDA VX LDA VC LDA.false..false..true. XC PBE EX PBE EC PBE VX PBE VC PBE.false..true..true. XC WC EX WC EC PBE VX WC VC PBE.false..true..false. XC PBESOL EX PBESOL EC PBESOL VX PBESOL VC PBESOL.false..true..true. XC MBJ EX LDA EC LDA VX MBJ VC MBJ.true..true..false. XC REVTPSS EX REVTPSS EC REVTPSS VX PBESOL VC PBESOL.true..true..false. XC MGGA MS EX MGGA MS EC MGGA MS VX PBE VC PBE.true..true..false. XC B3LYP EX B3LYP EC B3LYP VX B3LYP VC B3LYP.false..true..true. XC B3PW91 EX B3PW91 EC B3PW91 VX B3PW91 VC B3PW91.false..true..true. Table 7.3: XC shortcut-switches line 2: free format (only blanks are allowed as separator) RPRINT, H-mod, FFTopt, LUSE RPRINT NR2V no additional output R2V Exchange-correlation (case.r2v), Coulomb (case.vcoul) and total potentials (case.vtotal) are written as (r 2 V ) to a file for plotting with lapw5 (cp case.vtotal case.clmval; use VAL for normalization in case.in5) H-mod EECE Onsite Hartree-Fock (inside spheres) for selected electrons (see 4.5.7) HYBR Onsite Hybrid functionals (inside spheres) (see 4.5.7) FFTopt IFFT optional keyword, which lets you define the IFFTx mesh and an enhancement factor in the next line (necessary for runeece lapw) LUSE optional l-max value for the angular grid used in xcpot1. For standard LDA/GGA the recommended value is max L value of LM-list in case.in2 + 2; for EECE one should use a better, antialiased grid, thus a large negative LUSE-value is recommended (and set automatically by runeece lapw) line 3: free format (must be omitted when IFFT is not specified above) IFFTx, IFFTy, IFFTz, IFFTfactor, iprint

127 7.2. DFTD3 109 IFFTx,y,z IFFTfactor iprint FFT-mesh parameters in x,y,z directions for the calculation of the XC-potential in the interstitial region. Usually set automatically in init lapw (dstart). The ratio of the 3 numbers should be indirect proportional to the lattice parameters. ( determines these numbers automatically and takes only IFFTfactor into account) Multiplicative factor to the IFFT grid specified above. It needs to be enlarged for highly accurate GGA or meta-gga calculations as well as for systems with H atoms with small spheres. optional print switch. iprint=0 will greatly reduce case.output0 (in particular for lapw0 mpi). The following line is optional and can be omitted. It is used to introduce an electric field via a zig-zag potential (see J.Stahn et al. 2001): line 4: free format IFIELD, EFIELD, WFIELD IFIELD number of Fourier coefficients to model the zig-zag potential. Typically use IEFIELD=30; -999 lists available modes (form) of fields, and these modes can be specified by mode=iefield/1000. (default: mode=0) EFIELD value (amplitude) of the electric field. The electric field (in Ry/bohr) corresponds to EFIELD/c, where c is your c lattice parameter. WFIELD optional value for lambda (see output of IEFIELD=-999). 7.2 DFT-D3 (Calculate the dispersion energy with DFT-D3) dftd3 calculates the dispersion energy and forces using the semi-empirical DFT-D3 method of Grimme et al Since this method depends only on the positions of atoms (no dependence on the electron density) it is very fast and adds very little computer time. The dftd3 package is not included by default in WIEN2k, but can be downloaded from the website of the group of S. Grimme When compilation is done, the executable dftd3 has to be copied in the $WIENROOT directory Execution The program dftd3 is executed by invoking the command: x dftd Input The options for the dftd3 package have to be specified in the input file case.indftd3. If no input file is created by the user, then the script run(sp) lapw will automatically copy the default one (which is the recommended one) from $WIENROOT/SRC templates/: top of file: case.indftd method bj func default grad yes pbc yes abc no cutoff 95 cnthr 40 num no bottom of file:

128 110 CHAPTER 7. SCF CYCLE A short summary of the options is given below and more details can be found in the file man.pdf included in the dftd3 TAR file. Note that case.indftd3 is read by the C-SHELL script and that all data should be written in small letters. method : choice of the DFT-D method: bj (the recommended one), zero or old. func <functional> : three choices are possible: (a) default, which means the functional specified in case.in0 (possible only if the parameters s 6, s 8, etc. for this functional are available), (b) one of the functionals listed in the FORTRAN file dftd3.f (e.g., pbe or b-lyp) or (c) none, which means that the parameters s 6, s 8, etc. are read from the file.dftd3par.hostname created by the user in his home (not working) directory. Note that for hybrid functionals, it is mandatory to specify the functional name (default will not work). grad : yes or no for the calculation of the forces on the nuclei (necessary for the minimization of internal parameters). pbc : yes or no for periodic boundary conditions (pbc). It should be no for an isolated atom or molecule in a big box. abc : yes or no for the calculation of the three-body dispersion contribution with DFT-D3. cutoff <value> : The cutoff for the dispersion interaction. The default is 95 bohr. cnthr <value> : The cutoff for the coordination number CN. The default is 40 bohr. num : yes or no for the numerical (instead of analytical) calculation of forces. 7.3 ORB (Calculate orbital dependent potentials) This program was contributed by: P.Novák Inst. of Physics, Acad.Science, Prague, Czeck Republic Please make comments or report problems with this program to the WIEN-mailinglist. we will communicate the problem to the authors. If necessary, orb calculates the orbital dependent potentials, i.e. potentials which are nonzero in the atomic spheres only and depend on the orbital state numbers l, m. In the present version the potential is assumed to be independent of the radius vector and needs the density matrix calculated in lapwdm. Four different potentials are implemented in this package: LDA+U. There are three variants of this method, two of them are discussed in Novák et al LDA+U(SIC) - introduced by Anisimov et al. 1993, with an approximate correction for the self-interaction correction. This is probably best suited for strongly correlated systems and for a full potential method we recommend to use an effective U eff = U J; setting J = LDA+U(AMF) - introduced by Czyzyk and Sawatzky 1994 as Around the Mean Field method. (In Novák et al it is denoted as LDA+U(DFT)). This version is (probably) more suitable for metallic or less strongly correlated systems. 3. LDA+U(HMF) - in addition the Hubbard model in the mean field approximation, as introduced by Anisimov et al is also implemented. Note, however, that it is to be used with the LDA (not LSDA) exchange-correlation potential in spin polarized calculations!

129 7.3. ORB 111 All variants are implemented in the rotationally invariant way (Liechtenstein et al. 1995). If LDA+U is used in an unrestricted, general way, it introduces an orbital field in the calculation (in analogy to the exchange field in spin-polarized calculations, but it interacts with the orbital, instead of spin momentum). The presence of such an orbital field may lower the symmetry. In particular the complex version of LAPW1 must be used. Care is needed when dealing with the LDA+U orbital field. It may be quite large, and without specifying its direction it may fluctuate, leading to oscillations of scf procedure or/and to false solutions. It is therefore necessary to use it in combination with the spin-orbit coupling, preferably running first LSDA+(s-o) and then slowly switching on the LDA+U orbital field. If the LDA+U orbital polarization is not needed, it is sufficient to run real version of LAPW1, which then automatically puts the orbital field equal to zero. For systems without the center of inversion, when LAPW1 must be complex, an extra averaging of the LDA+U potential is necessary. Orbital polarization. The additional potential has the form (Brooks 1985, Eriksson et al. 1989): V OP = c OP < L z > l z (7.1) where c OP is the orbital polarization parameter, < L z > is projection of the orbital momentum on the magnetization direction and l z is single electron orbital momentum component z parallel to M. Exact exchange and Hybrid methods: see Tran et al and Interaction with the external magnetic field. In this case the additional potential has a simple form: V Bext = µ B Bext ( l + 2 s). (7.2) The interaction with the electronic spin is taken into account by shifting the spin up and spin down exchange correlation potentials in LAPW0 by the energy +µ B B ext µ B B ext, respectively. The interaction of B ext with spin could be as well calculated using the Fixed spin moment method. For an interaction with the orbital momentum it is necessary to specify the atoms and angular momentum numbers for which this interaction will be considered. Caution is needed when considering interaction of the orbital momentum with B ext in metallic or metallic-like systems. For the analysis see the paper by Hirst 1997 In all cases the resulting potential for a given atom and orbital number l is a Hermitian, (2l + 1)x(2l + 1) matrix. In general this matrix is complex, but in special cases it may be real. For more information see also section Execution The program orb is executed by invoking the command: x orb [ -up/-dn/-du ] or orb up/dnorb.def Dimensioning parameters The following parameters are used (collected in file param.inc): LABC NRAD highest l+1 value of orbital dependent potentials number of radial mesh points Input Since this program can handle three different cases, examples and descriptions of case.inorb for all cases are given below:

130 112 CHAPTER 7. SCF CYCLE Input for all potentials line 1: free format nmod,natorb,ipr nmod natorb ipr defines the type of potential 1...LDA+U, 2...OP, 3...B ext number of atoms for which orbital potential V orb is calculated printing option, the larger ipr, the longer the output line 2: (A5,f8.2) mixmod,amix mixmod PRATT or BROYD (should not be changed, see MIXER for more information) amix coefficient for the Pratt mixing of V orb This option is now only used for testing. The mixing should be set to PRATT, 1.0 line 3: free format iatom(i),nlorb(i),(lorb(li,i),li=1,nlorb(i)) iatom nlorb lorb index of atom in struct file number of orbital moments for which Vorb shall be applied orbital numbers (repeated nlorb-times) 3rd line repeated natorb-times Input for LDA+U (nmod=1) line 4: free format nsic defines double counting correction nsic=0 AMF method (Czyzyk et al. 1994) nsic=1 SIC method (Anisimov et al. 1993, Liechtenstein et al. 1995) nsic=2 HMF method (Anisimov et al. 1991) line 5: free format U(li,i), J(li,i) Coulomb and exchange parameters, U and J, for LDA+U in Ry for atom type i and orbital number li. We recommend to use U eff only. 5th line repeated natorb-times, for each natorb repeated nlorb-times Example of the input file for NiO (LDA+U included for two inequivalent Ni atoms that have indexes 1 and 2 in the structure file): top of file: case.inorb nmod, natorb, ipr PRATT,1.0 mixmod, amix iatom nlorb, lorb iatom nlorb, lorb 1 nsic (LDA+U(SIC) used) U J U J bottom of file:

131 7.3. ORB 113 Input for Orbital Polarization (nmod=2) line 4: (free format) nmodop defines mode of OP 1 average L z taken separately for spin up, spin down 0 average L z is the sum for spin up and spin down line 5: (free format) Ncalc(i) 1 Orb.pol. parameters are calculated ab-initio 0 Orb.pol. parameters are read from input this line is repeated natorb-times line 6: (free format) (only if Ncalc=0, then repeated nlorb-times) pop(li,i) OP parameter in Ry line 7: (free format) xms(1), xms(2), xms(3) direction of magnetization expressed in terms of lattice vectors Example of the input file for NiO (total < L z > used in (1), OP parameters calculated ab-initio, M along [001]): top of file: case.inorb nmod, natorb, ipr PRATT, 1.0 mixmod, amix iatom nlorb, lorb iatom nlorb, lorb 0 nmodop 1 Ncalc 1 Ncalc direction of M in terms of lattice vectors bottom of file Input for interaction with B ext (nmod=3) line 4: (free format) B ext external field in Tesla line 5: (free format) xms(1), xms(2), xms(3) direction of magnetization expressed in terms of lattice vectors Example of the input file for NiO, (B ext = 4 T, along [001]): top of file: case.inorb nmod, natorb, ipr PRATT, 1.0 mixmod, amix iatom nlorb, lorb iatom nlorb, lorb 4. Bext in T direction of Bext in terms of lattice vectors bottom of file

132 114 CHAPTER 7. SCF CYCLE 7.4 HF (Calculates the hybrid orbitals and eigenvalues) hf calculates the orbitals and eigenvalues for hybrid functionals using the second-variational procedure, i.e., the semilocal orbitals generated by lapw1 are used as basis functions for the secondvariational Hamiltonian (Tran and Blaha 2011). The hybrid orbitals are stored in case.vectorhf (full Brillouin zone). Since calculations with hybrid functionals are much more expensive than with semilocal functionals, it is important to choose carefully the values of the various parameters (nband, gmax, lmaxe and lmaxv) in case.inhf because the computational time will depend strongly on them. Choosing carefully the value of a parameter means to determine (by test calculations) the lowest value which is enough for the accuracy that is needed. This will depend on the solid, the property (e.g., lattice constant or band gap) and the RMT. The more the RMT is small, the more lmaxe and lmaxv can be chosen to be small, while gmax will need to be increased. Setting up a hybrid calculation needs some additional considerations and is described in detail in Sec Parallel execution (fine grain MPI and on the k-point level) is also possible and is described in Secs and 5.5. Beside the selfconsistent calculations, it is also possible to calculate the total energy with hybrid functionals non-selfconsistently (switch -nonself) and to calculate the hybrid eigenvalues (but not the orbitals) in a cheap way (switch -diaghf) Execution The program hf is executed by invoking the command: x hf [-up/dn -c -p -band -diaghf -nonself -newklist -redklist] or hf hf.def or hfc hf.def Input top of file: case.inhf alpha T screened (T) or unscreened (F) lambda xx nband 6 gmax 3 lmaxe 3 lmaxv 1d-3 tolu bottom of file: Interpretive comments on this file are as follows: line 1: free format α fraction (α [0, 1]) of Hartree-Fock exchange line 2: free format screening if set to F (false), no screening is applied to the exchange. If set to T (true), the exchange is screened by means of the Yukawa potential and the screening parameter λ will have to be specified in the next line. Note, that unscreend HF requires a denser k-mesh than screened HF.

133 7.4. HF 115 line 3: free format λ screening parameter in bohr 1. This line should be present only if screening is set to T (true) in line 2. With the value λ = bohr 1, the results are very close to the values from the HSE06 hybrid functional (Tran and Blaha 2011). Values for λ smaller than or larger than 5 can eventually lead to suspicious results due to numerical instabilities. line 4: free format nband the number of bands used for the 2nd variational procedure. nband should be at least equal to the number of (partially) occupied bands plus one. The choice for nband will depend strongly on the studied property and accuracy needed. If the switch -diaghf is used, then the accuracy of the eigenvalues will not depend on the value of nband, therefore nband can be chosen as the smallest value that you want (but still at least to the number of occupied bands plus one) line 5: free format gmax magnitude of the largest vector G in the Fourier expansion of the product of two orbitals and the generated potential in the interstitial region (Eqs. (13) and (14) in Tran and Blaha 2011). gmax=6 can eventually represent a good compromise between computational time and accuracy. line 6: free format lmaxe maximum value of the angular momentum for the expansion in spherical harmonics of the product of two orbitals and the generated potential inside the atomic spheres (Eqs. (13) and (14) in Tran and Blaha 2011). lmaxe=3 or 4 are usually large enough for good accuracy for light elements. For systems with f electrons, the value lmaxe=6 may eventually be necessary. line 7: free format lmaxv maximum value of the angular momentum of the expansion of the orbitals (l i in Eq. (15) in Tran and Blaha 2011). The value should be at least equal to the largest chemical l present in the system. line 8: free format tolerance below this value, the double radial integrals in Eq. (26) (Tran and Blaha 2011) are neglected. With tolu=1d-3 (or even 1d-2) not much accuracy is lost.

134 116 CHAPTER 7. SCF CYCLE 7.5 LAPW1 (generates eigenvalues and eigenvectors) lapw1 sets up the Hamiltonian and the overlap matrix (Koelling and Arbman 75) and finds by diagonalization eigenvalues and eigenvectors which are written to case.vector. Besides the standard LAPW basis set, also the APW+lo method (see Sjöstedt et al 2000, Madsen et al. 2001) is supported and the basis sets can be mixed for maximal efficiency. If the file case.vns exists (i.e. non-spherical terms in the potential), a full-potential calculation is performed. For structures without inversion symmetry, where the hamilton and overlap matrix elements are complex numbers, the corresponding program version lapw1c must be used in connection with lapw2c. Since usually the diagonalization is the most time consuming part of the calculations, two options exist here. In WIEN2k we include highly optimized modifications of LAPACK routines. We call all these routines full diagonalization, but we also provide an option to do an iterative diagonalization using a new preconditioning of a block-davidson method (see Singh 89 and Blaha et al. 09). The scheme uses an old eigenvector from the previous scf-iteration, and produces approximate (but usually still highly accurate) eigenvalues/vectors. The preconditioner (inverse of (H λs) can be calculated at the first iterative step (which will therefore take longer than subsequent iterative steps), stored on disk (case.storehinv) and reused in all subsequent scf-iterations (until the next full diagonalization or when it is recreated (x lapw1 -it -nohinv0)). Usually this is the fastest scheme, but storage of case.storehinv can be large (and slow when you have a slow network) and when the Hamiltonian changes too much, performance may degrade. Alternatively, the preconditioner can be recalculated all the time (x lapw1 -it -nohinv). Depending on the ratio of matrix size to number of eigenvalues (cpu time increases linearly with the number of eigenvalues, but a sufficiently large number is necessary to ensure convergence) a significant speedup compared to full diagonalization (LAPACK) can be reached. Iterative diagonalization is activated with the -it switch in x lapw1 -it or run lapw -it. Often the preconditioner is so efficient, that it does not need to be recalculated, even within a structural optimization and one can use min lapw -j run lapw -I -fc 1 -it. In some cases it is preferable to use min lapw -j run lapw -I -fc 1 -it1, which will recreate case.storehinv, or do not store these files at all using min lapw -j run lapw -I -fc 1 -it -nohinv Parallel execution (fine grain and on the k-point level) is also possible and is described in detail in Sec The switch -nohns skips the calculation of the nonspherical matrix elements inside the sphere. This may be used to save computer time during the first scf cycles Execution The program lapw1 is executed by invoking the command: x lapw1 [-c -up dn -it -nohinv -nohinv0 -p -nohns -orb -band -nmat only -nmr] or lapw1 lapw1.def or lapw1c lapw1.def In cases without inversion symmetry, the default input filename is case.in1c. For 2-window (not recommended) semi-core calculations the lapw1s.def file uses a case.in1s file and creates the files case.output1s and case.vectors. For the spin-polarized case lapw1 is called twice with uplapw1.def and dnlapw1.def. To all relevant files the keywords up or dn are appended (see the fcc Ni test case in the WIEN2k package) Dimensioning parameters The following parameters (collected in file param.inc r or param.inc c) are used: LMAX highest l+1 in basis function inside sphere (consistent with input in case.in1)

135 7.5. LAPW1 117 LMMX number of LM terms in potential (should be at least NCOM-1) LOMAX highest l for local orbital basis (consistent with input in case.in1) NGAU number of Gaunt coefficients for the non-spherical contributions to the matrix elements NMATMAX maximum size of H,S-matrix (defines size of program, should be chosen according to the memory of your hardware, see chapter !) NRAD number of radial mesh points NSLMAX highest l+1 in basis functions for non-muffin-tin matrix elements (consistent with input in case.in1).if set larger than 5, parameter MAXDIM (modules.f) and LO- MAX=8, P(10,10) (gaunt2.f) must also be increased. NSYM order of point group NUME maximum number of energy eigenvalues per k-point NVEC1 defines the largest triple of integers which define reciprocal NVEC2 K-vectors when multiplied with the reciprocal Bravais matrix NVEC3 restrict output for mpi-jobs, limits the number of case.output1 X proc XXX files to restrict output Input Below a sample input is shown for T io 2 (rutile), one of the test cases provided in the WIEN2k package. The input file is written automatically by LSTART, but was modified to set APW only for Ti-3d and O-2p orbitals top of file: case.in WFFIL EF= (WFPRI,WFFIL,SUPWF ; wave fct. print,file,suppress (R-mt*K-max; MAX l, max l for hns ) (global energy parameter E(l), with 5 other choices, LAPW) CONT 0 ENERGY PARAMETER for s, LAPW CONT 0 ENERGY PARAMETER for s-local orbital, LAPW-LO CONT 0 ENERGY PARAMETER for p LAPW CONT 0 ENERGY PARAMETER for p-local orbitals LAPW-LO CONT 1 APW (global energy parameter E(l), with 1 other choice, LAPW) STOP 0 LAPW CONT 0 LAPW-LO CONT 1 APW K-VECTORS FROM UNIT: emin/emax/nband 1.d spro_limit for it.diag., lambda for it.diag bottom of file Interpretive comments follow: line 1: free format switch, EF switch WFFIL standard option, writes wave functions to file case.vector (needed in lapw2) SUPWF suppresses wave function calculation (faster for testing eigenvalues only) WFPRI prints eigenvectors to case.output1 and writes case.vector (produces long outputs!) EF optional input. If EF= key is present, lapw1 reads EF and sets the default energy parameters (0.3) to EF-0.2 or EF+0.2 (for a high- LO ) Ry. line 2: free format

136 118 CHAPTER 7. SCF CYCLE rkmax, lmax, lnsmax rkmax lmax lnsmax R mt K max determines matrix size (convergence), where Kmax is the plane wave cut-off, Rmt is the smallest of all atomic sphere radii. Usually this value should be between 5 and 9 (APW+lo) or (LAPWbasis) (Kmax 2 would be the plane wave cut-off parameter in Ry used in pseudopotential calculations.) Note that d (f) wavefunctions converge slower than s and p. For systems including hydrogen with short bondlength and thus a very small R mt (e.g. 0.7 a.u.), RKmax = 3 might already be reasonable, but convergence must be checked for a new type of system. Note, that the actual matrix size is written on case.scf1. It is determined by whatever is smaller, the plane wave cut-off (specified with RKmax) or the maximum matrix dimension NMATMAX, (see previous section). maximum l value for partial waves used inside atomic spheres (should be between 8 and 12) maximum l value for partial waves used in the computation of nonmuffin-tin matrix elements (lnsmax=4 is quite good) line 3: free format Etrial, ndiff, Napw Etrial ndiff Napw default energy used for all E l to obtain u l (r, E l ) as regular solution of the radial Schrödinger equation [used in equ.2.4,2.7] (see figure 7.1). number of exceptions (specified in the next ndiff lines) 0... use LAPW basis, 1... use APW-basis for all global l values of this atom. We recommend to use LAPW here. line 4: format(i2,2f10.5,a4) l, El, de, switch, NAPWL l El de switch CONT STOP l of partial wave E l for L=l energy increment de=0: this E(l) overwrites the default energy (from line 3) de 0: a search for a resonance energy using this increment is done. The radial function u l (r, E) up to the muffin-tin radius RMT varies with the energy. A typical case is schematically shown in Fig At the bottom of the energy bands u has a zero slope (bonding state), but it has a zero value (antibonding state) at the top of the bands. One can search up and down in energy starting with E l using the increment de to find where u l (R MT, E) changes sign in value to determine E top and in slope to specify E bottom. If both are found E l is taken as the arithmetic mean and replaces the trial energy. Otherwise E l keeps the specified value. For E top and E bottom bounds of +1 and -10 Ry are defined respectively, and if they are not found, they remain at the initial value set to used only if de.ne.0 calculation continues, even if either E top or E bottom are not found calculation stops if not both E top and E bottom are found (especially useful for semi-core states)

137 7.5. LAPW1 119 NAPWL 0... use LAPW basis, 1... use APW-basis for this l value of this atom. We recommend to use APW+lo when the corresponding wavefunction is localized and thus difficult to converge with standard LAPW (like 3d functions) and/or when the respective atomic sphere is small compared to the other spheres in the unit cell. u (r,e) l E bottom E E top E l E l R MT E top r E bottom DOS Figure 7.1: Schematic dependence of DOS and u l (r, E l ) on the energy >>>:line 4 is repeated ndiff times (see line 3) for each exception. If the same l value is specified twice, local orbitals are added to the (L)APW basis. The first energy (E 1 ) is used for the usual LAPW s and the second energy (E 2 ) for the LOs, which are formed according to (see equ. 2.7): u E1 + u E1 + u E2. Note: The default energy parameters (0.30) are replaced by an energy E F 0.2 if the EF-switch was read before. Please read also the comments about run lapw in section In addition, you may want to change the automatically created input and add d- or f-local orbitals to reduce the linearization error (e.g. in late transition metals you could put E 3d at 0.0 and 1.0 Ry) or s, p, d, and/or f-los at very high energy (e.g Ry) to better describe unoccupied states. >>>:lines 3 and 4 are repeated for each non equivalent atom line 5: format (20x,i1,2f10.1,i6) unit-number, Emin, Emax nband unitnumber EMIN, EMAX nband file number from which the k-vectors in the irreducible wedge of the Brillouin zone are read. Default is 4, for which the corresponding information is contained in case.klist (generated by KGEN). Should not be changed. energy window in which eigenvalues shall be searched (overrides setting in case.klist. A small window saves computer time, but it also limits the energy range for the DOS calculation of unoccupied states. number of eigenvalues calculated with iterative diagonalization. Set automatically to nband = ne in lstart. Larger values will lead to more cpu-time. (Optional input) line 6: free format; optional input line, but necessary if k-vectors are read from unit 5 spro limit, lambda iter spro limit limit for detection of linear dependency for iterative diagonalization (optional input), typical around 1.d-15)

138 120 CHAPTER 7. SCF CYCLE lambda iter optional λ value for preconditioner of iterative diagonalization (see above). By default we use λ = 0, but in some cases convergence can be improved by a small (around 1.0) positive or negative λ line 7: format (A10,4I10,3F5.2); (only when unit-number=5, not recommended, use unit 4 and case.klist) name, ix,iy,iz, idv, weight name name of k-vector (optional) >>>: the last line must be END!! ix,iy,iz, defines the k-vector, where x= ix/idv etc. We use cartesian coordinates idv in units of 2π/a, 2π/b, 2π/c for P,C,F and B cubic, tetragonal and orthorhombic lattices, but internal coordinates for H and monoclinic/triclinic lattices weight of k-vector (order of group of k) >>>: line 7 is repeated for each k-vector in the IBZ. The utility program kgen (see section 6.5) provides a list of such vectors (on a tetrahedral mesh) in case.klist. >>>: the last line must be END 7.6 LAPWSO (adds spin orbit coupling) lapwso includes spin-orbit (SO) coupling in a second-variational procedure and computes eigenvalues and eigenvectors (stored in case.vectorso) using the scalar-relativistic wavefunctions from lapw1. For reference see Singh 94 and Novák 97. The SO coupling must be small, as it is diagonalized in the space of the scalar relativistic eigenstates. For large spin orbit effects it might be necessary to include many more eigenstates from lapw1 by increasing EMAX in case.in1 (up to 10 Ry!). We also provide an additional basisfunction, namely a relativistic-lo (RLO) with a p 1/2 radial wavefunction, which improves the basis and removes to a large degree the dependency of the results on EMAX and RMT (see Kuneš et al. 2001). It is particular helpfull for heavier atoms with semicore p-states, but it must not be used for EFG calculations. SO is considered only within the atomic spheres and thus the results may depend to some extent on the choice of atomic spheres radii. The nonspherical potential is neglected when calculating dv dr. Orbital dependent potentials (LDA+U, EECE or OP) can be added to the hamiltonian in a cheap and simple way. In spin-polarized calculations the presence of spin-orbit coupling may reduce symmetry and even split equivalent atoms into non-equivalent ones. It is then necessary to consider a larger part of the Brillouin zone and the input for lapw2 should also be modified since the potential has lower symmetry than in the non-relativistic case. The following inputs may change: case.struct case.klist case.kgen case.in2c case.in1 We recommend to use initso (see Sec ) which helps you together with symmetso (see Sec.9.1) to setup spinorbit calculations. Note: SO eigenvectors are complex and thus lapw2c must be used in a selfconsistent calculation.

139 7.6. LAPWSO Execution The program lapwso is executed by invoking the command: x lapwso [ -up -p -c -orb] or lapwso lapwso.def where here -up indicates a spin-polarized calculation (no -dn is needed, since spin-orbit will mix spin-up and dn states in one calculation) Dimensioning parameters The following parameters are used (collected in file module.f): FLMAX constant = 3 LMAX highest l of wave function inside sphere (consistent with lapw1) LOMAX max l for local orbital basis NRAD number of radial mesh points Input A sample input for lapwso is given below. It will be generated automatically by initso top of file: case.inso WFFIL llmax,ipr,kpot Emin, Emax h,k,l (direction of magnetization) 2 number of atoms with RLO STOP atom-number, E-param for RLO STOP atom-number, E-param for RLO 1 2 number of atoms without SO, atomnumbers bottom of file Interpretive comments on this file are as follows: line 1: format(a5) switch WFFIL wavefunctions will also be calculated for scf-calculation. Otherwise only eigenvalues are calculated. line 2: free format LLMAX, IPR, KPOT LLMAX maximum l for wavefunctions IPR print switch, larger numbers give additional output. KPOT 0 V(dn) potential is used for < dn V dn > elements, V(up) for < up V up > and [V(dn)+V(up)]/2 for < up V dn >. 1 averaged potential used for all matrix elements. line 3: free format Emin, Emax

140 122 CHAPTER 7. SCF CYCLE Emin Emax minimum energy for which the output eigenvectors and eigenenergies will be printed (Ry) maximum energy line 4: free format h,k,l vector describing the direction of magnetization. For R lattice use h,k,l in rhombohedral coordinates (not in hexagonal) line 5: free format nlr number of atoms for which a p 1/2 LO should be added line 6: free format nlri, El, de, switch nlri El de switch CONT STOP atom-number for which RLO should be added E l for L=l energy increment (see lapw1) used only if de.ne.0 calculation continues, even if either E top or E bottom are not found calculation stops if not both E top and E bottom are found (especially useful for semi-core states) >>>: line 6 must be repeated nlr times (or should be omitted if nlr=0). line 7: free format noff, (iatoff(i),i=1,noff) noff iatoff number of atoms for which SO is switched off (for light elements, saves time) atom-numbers 7.7 LAPW2 (generates valence charge density expansions) lapw2 uses the files case.energy and case.vector and computes the Fermi-energy (for a semiconductor E F is set to the valence band maximum) and the expansions of the electronic charge densities in a representation according to eqn for each occupied state and each k-vector; then the corresponding (partial) charges inside the atomic spheres are obtained by integration. In addition Pulay-corrections to the forces at the nuclei are calculated here. For systems without inversion symmetry you have to use the program lapw2c (in connection with lapw1c). The partial charges for each state (energy eigenvalue) and each k-vector can be written to files case.help031, case.help032 etc., where the last digit gives the atomic index of inequivalent atoms (switch -help files). Optionally these partial charges are also written to case.qtl (switch -qtl). For meta-gga calculations energy densities are written to case.vrepval(switch -vresp). In order to get partial charges for bandstructure plots, use -band, which sets the QTL option and uses ROOT in case.in2. Several other switches change the input file case.in2 temporarely and are described there.

141 7.7. LAPW Execution The program lapw2 is executed by invoking the command: x lapw2 [-c -up dn -p -so -qtl -fermi -efg -hf -band -eece -vresp -help files -emin X -all X Y] or lapw2 lapw2.def [proc#] or lapw2c lapw2.def [proc#] where proc# is the i-th processor number in case of parallel execution (see Fig. 5.2). The -so switch sets -c automatically. For complex calculations case.in2c is used. For a spin-polarized case see the fcc Ni test case in the WIEN2k package Dimensioning parameters The following parameters are used (collected in file modules.f): IBLOCK Blocking parameter (32-255) in l2main.f, optimize for best performance LMAX2 highest l in wave function inside sphere (smaller than in lapw1, at present must be.le. 8) LOMAX max l for local orbital basis NCOM number of LM terms in density NGAU max. number of Gaunt numbers NRAD number of radial mesh points restrict output for mpi-jobs, limits the number of case.output2 X proc XXX files to restrict output Input A sample input for lapw2 is listed below, it is generated automatically by the programs lstart and symmetry top of file: case.in TOT (TOT,FOR,QTL,EFG) (EMIN, # of electrons,esepermin, ESEPER0,iqtlsave) TETRA 0.0 (EF-method (ROOT,TEMP,GAUSS,TETRA,ALL),value) (GMAX) FILE (NOFILE, optional) bottom of file Interpretive comments on this file are as follows: line 1: format(2a5) switch, EECE switch TOT total valence charge density expansion inside and outside spheres FOR same as TOT, but in addition a Pulay force contribution is calculated (this option costs extra computing time and thus should be performed only at the final scf cycles, see run lapw script in sec ) QTL partial charges only (generates file case.qtl for DOS calculations), set automatically by switch -qtl

142 124 CHAPTER 7. SCF CYCLE EECE EFG ALM CLM FERMI computes decomposition of electric field gradient (EFG), contributions from inside spheres (the total EFG is computed in lapw0), set automatically by switch -efg. this generates two files, case.radwf and case.almblm, where the radial wavefunctions and the A lm, B lm, C lm coefficients of the wavefunction inside spheres are listed. The file case.almblm can get very big. CLM charge density coefficients only Fermi energy only, this produces weight files for parallel execution and for the optics and lapwdm package, set automatically by switch -fermi. >>>: TOT and FOR are the standard options, QTL is used for density of states (or energy bandstructure) calculations, EFG for analysis, while FOURI, CLM are for testing only. if set to EECE, calculates the density for specified atoms and angular momentum only. Used for exact-exchange or hybrid-calculations, usually set automatically by runsp lapw -eece line 2: free format emin, ne, esepermin, eseper0, iqtlsave emin ne esepermin eseper0 iqtlsave lower energy cut-off for defining the range of occupied states, can be set termporarely to X by switch -emin X or -all X Y number of electrons (per unit cell) in that energy range LAPW2 tries to find the mean energies for each l channel, for both the valence and the semicore states. To define valence and semicore it starts at (EF - esepermin ) and searches for a gap with a width of at least eseper0 and defines this as separation energy of valence and semicore minimum gap width (see above). The values esepermin and eseper0 will only influence results if the option -in1new is used optional value, checks if the low-energy bandranges (below -2 Ry) are narrow (below 0.2 Ry) and stops (iqtlsave=1 = default) / does not stop (iqtlsave=0). You may have to switch it off for extreme pressures, because then you may have large band width even for semi-core states. line 3: format(a5,f10.5) efmod, eval efmod determines how E F is determined ROOT E F is calculated and k space integration is done by root sampling (this can be used for insulators, but for metals poor convergence is found) TEMP E F is calculated where each eigenvalue is temperature broadened using a Fermi function with a broadening parameter of eval Ry. The total energy is corrected corresponding to T=0K. (e.g. eval=0.002 Ry gives good total energy convergence, but has no physical justification) TEMPS E F is calculated where each eigenvalue is temperature broadened using a Fermi function with a broadening parameter of eval Ry. The total energy is corrected by -TS corresponding to the temperature specified by eval (e.g. eval=0.002 Ry corresponds to about 40 C) GAUSS E F is calculated as above but a Gaussian smearing method is used with a width of eval Ry. (e.g. eval=0.002 gives good total energy convergence, but has no physical justification).

143 7.7. LAPW2 125 eval TETRA ALL E F is calculated and k space integration is done by the modified (if eval is.eq. 0) or standard (eval.ge. 100) tetrahedron-method (Blöchl 94). This standard scheme is recommended for optic. In this case the file case.kgen, consistent with the k-mesh used in lapw1, must be provided (see Sec. 7.5). This is the recommended option although convergence may be slower than with Gauss- or temperature-smearing. All states up to eval are used. This can be used to generate charge densities in a specified energy interval, can be set termporarely by switch -all X Y. when efmod is set to TEMP(S) (eval=0 will lead to room temperature broadening, Ry) or GAUSS, eval specifies the width of the broadening (in Ry), if efmod is set to ALL, eval specifies the upper limit of the energy window (in Ry; can be set termporarely by switch -all X Y), if efmod is set to TETRA, eval.ge. 100 specifies the use of the standard tetrahedron method instead of the modified one (see above). By default, TETRA will average over partially occupied degenerate states at EF with a degeneracy criterium D = 1.d-6. You can modify this by setting eval equal to your desired D (or 100+D). optional line 3a: free format (ONLY when EECE is set) nat rho number of atoms for which a specific density should be calculated optional line 3b: free format (ONLY when EECE is set) jatom rho, l rho jatom rho l rho index of atom for which a specific density should be calculated angular momentum l-value for which a specific density should be calculated >>>line 3b: must be repeated nat rho times line 4: format (121(I3,I2)) L,M LM values of lattice harmonics expansion (equ. 2.10), defined according to the point symmetry of the corresponding atom; generated in SYMMETRY, MUST be consistent with the local rotation matrix defined in case.struct (details can be found in Kara and Kurki-Suonio 81). CAUTION: additional LM terms which do not belong to the lattice harmonics will in general not vanish and thus such terms must be omitted. Automatic termination of the lm series occurs when a second 0,0 pair appears within the list. When you change the l, m list during an SCF calculation the Broyden-Mixing is restarted in MIXER. >>>line 4: must be repeated for each inequivalent atom Symmetry LM combinations , 4 0, 4 4, 6 0, 6 4,-3 2, 6 2, 6 6,-7 2,-7 6, 8 0, 8 4, 8 8,-9 2,-9 6,-9 4,-9 8,10 0, 10 4,10 8, 10 2, 10 6, M3 0 0, 4 0, 4 4, 6 0, 6 4, 6 2, 6 6, 8 0, 8 4, 8 8,10 0, 10 4,10 8, 10 2, 10 6, , 4 0, 4 4, 6 0, 6 4, 8 0, 8 4, 8 8,-9 4,-9 8,10 0, 10 4, M 0 0, 4 0, 4 4, 6 0, 6 4,-3 2,-7 2,-7 6, 8 0, 8 4, 8 8,-9 2,-9 6,10 0, 10 4,10 8 M3M 0 0, 4 0, 4 4, 6 0, 6 4, 8 0, 8 4, 8 8,10 0, 10 4,10 8 Table 7.50: LM combinations of Cubic groups (3 (111)) direction, requires positive atomic index in case.struct. Terms that should be combined (Kara and Kurki-Suonio 81) must follow one another.

144 126 CHAPTER 7. SCF CYCLE Symmetry Coordinate axes Indices of Y ±LM crystal system 1 any ALL (±l,m) triclinic -1 any (±2l,m) 2 2 z (±l,2m) monoclinic M m z (±l,l-2m) 2/M 2 z, m z (±2l,2m) z, 2 y, (2 x) (+2l,2m), (-2l+1,2m) orthorhombic MM2 2 z, m y, (2 x) (+l,2m) MMM 2 z, m y, 2 x (+2l,2m) 4 4 z (±l,4m) tetragonal -4-4 z (±2l,4m), (±2l+1,4m+2) 4/M 4 z, m z (±2l,4m) z, 2 y, (2 x) (+2l,4m), (-2l+1,4m) 4MM 4 z, m y, (2 x) (+l,4m) -42M -4 z, 2 x (m=xy yx) (+2l,4m), (-2l+1,4m+2) 4MMM 4 z, m z, m x (+2l,4m) 3 3 z (±l,3m) rhombohedral -3-3 z (±2l,3m) 32 3 z, 2 y (+2l,3m), (-2l+1,3m) 3M 3 z, m y (+l,3m) -3M -3 z, m y (+2l,3m) 6 6 z (±l,6m) hexagonal -6-6 z (+2l,6m), (±2l+1,6m+3) 6/M 6 z, m z (±2l,6m) z, 2 y, (2 x) (+2l,6m), (-2l+1,6m) 6MM 6 z, m y, (m x) (+l,6m) -62M -6 z, m y, (2 x) (+2l,6m), (+2l+1,6m+3) 6MMM 6 z, m z, m y, (m x) (+2l,6m) Table 7.51: LM combination and local coordinate system of non-cubic groups (requires negative atomic index in case.struct) line 5: free format GMAX max. G (magnitude of largest vector) in charge density Fourier expansion. For systems with short H bonds larger values (e.g. GMAX up to 25) could be necessary. Calculations using GGA (potential option 13 or 14 in case.in0) should also employ a larger GMAX value (e.g. 14), since the gradients are calculated numerically on a mesh determined by GMAX. When you change GMAX during an scf calculation the Broyden-Mixing is restarted in mixer. line 6: A4 reclist FILE writes list of K-vectors into file case.recprlist or reuses this list if the file exists. The saved list will be recalculated whenever GMAX, or a lattice parameter has been changed. NOFILE always calculate new list of K-vectors 7.8 SUMPARA (summation of files from parallel execution) sumpara is a small program which (in parallel execution of WIEN2k) sums up the densities (case.clmval *) and quantities from the case.scf2 * files of the different parallel runs Execution The program sumpara is executed by invoking the 2 commands as follows: x sumpara -d [-up/-dn/-du] and then sumpara sumpara.def # of proc where # of proc is the numbers of parallel processors used. It is usually called automatically from lapw2para or x lapw2 -p Dimensioning parameters

145 7.9. LAPWDM LAPWDM (calculate density matrix) This program was contributed by: J.Kuneš and P.Novák Inst. of Physics, Acad.Science, Prague, Czeck Republic Please make comments or report problems with this program to the WIEN-mailinglist. we will communicate the problem to the authors. If necessary, lapwdm calculates the density matrix needed for the orbital dependent potentials generated in orb. Optionally it also provides orbital moments, orbital and dipolar contributions to the hyperfine field (only for the specified atoms AND orbitals). It calculates the average value of the operator X which behaves in the same way as the spin-orbit coupling operator: it must be nonzero only within the atomic spheres and can be written as a product of two operators - radial and angular: X = X r (r) X ls ( l, s) X r (r) and X ls ( l, s) are determined by RINDEX and LSINDEX in the input as described below: RINDEX=0 LSINDEX=0: the density matrix is calculated (this is needed for LDA+U calculations) RINDEX=1 LSINDEX=1: <X> is number of electrons inside the atomic sphere (for test) RINDEX=2 LSINDEX=1: <X> is the < 1/r 3 > expectation value inside the atomic sphere RINDEX=1 LSINDEX=2: <X> is the projection of the electronic spin inside the atomic sphere (must be multiplied by g=2 to get the spin moment) RINDEX=1 LSINDEX=3: <X> is the projection of the orbital moment inside the atomic sphere (in case of SO-calculations WITHOUT LDA+U) RINDEX=3 LSINDEX=3: <X> is the orbital part of the hyperfine field at the nucleus (for a converged calculation at the very end) RINDEX=3 LSINDEX=5: <X> is the spin dipolar part of the hyperfine field at the nucleus (for a converged calculation at the very end) To use the different operators, set the appropriate input. More information and extentions to operators of similar behavior may be obtained directly from P. Novák (2006). (RINDEX=3 includes now an approximation to the relativistic mass enhancement and LSINDEX=5 includes nondiagonal terms) lapwdm needs the occupation numbers, which are calculated in lapw2. Note: You must not use ROOT in case.in2 for that purpose Execution The program lapwdm is executed by invoking the command: x lapwdm [ -up/dn -p -c -so -hf] or lapwdm lapwdm.def Dimensioning parameters The following parameters are used (collected in file param.inc):

146 128 CHAPTER 7. SCF CYCLE FLMAX constant = 3 LMAX highest l of wave function inside sphere (consistent with lapw1) LABC highest l of wave function inside sphere where SO is considered LOMAX max l for local orbital basis NRAD number of radial mesh points Input A sample input for lapwdm is given below top of file: case.indm Emin cutoff energy 1 number of atoms for which density matrix is calculated index of 1st atom, number of L s, L1 0 0 r-index, (l,s)-index bottom of file Interpretive comments on this file are as follows: line 1: free format emin lower energy cutoff (usually set to very low number). line 2: free format natom number of atoms for which the density matrix is calculated line 3: free format iatom, nl, l iatom nl l index of atom for which the density matrix should be calculated number of l-values for which the density matrix should be calculated l-values for which the density matrix should be calculated line 3 is repeated natom times t line 4: free format, optional RINDEX, LSINDEX RINDEX 0-3, as described in the introduction to lapwdm LSINDEX0-5, as described in the introduction to lapwdm 7.10 LCORE (generates core states) lcore is a modified version of the Desclaux (69, 75) relativistic LSDA atomic code. It computes the core states (relativistically including SO, or non-relativistically if NREL is set in case.struct) for the current spherical part of the potential (case.vsp). It yields core eigenvalues, the file case.clmcor with the corresponding core densities, and the core contribution to the atomic forces Execution The program lcore is executed by invoking the command:

147 7.10. LCORE 129 lcore lcore.def or x lcore [-up -dn] For the spin-polarized case see fcc Ni on the distribution tape. If case.incup and case.incdn are present for spin-polarized calculations, different core-occupation ( open core approximation for 4f states or spin-polarized core-holes) for both spins are possible Dimensioning parameters The following parameter is listend in file param.inc: NRAD number of radial mesh points Input Below is a sample input (written automatically by lstart) for T io 2 (rutile), one of the test cases provided with the WIEN2k package. In case of a open core calculation (eg. for 4f states) you may need spin-polarized case.inc files in order to define different configurations for spin-up and dn. Create two files case.incup and case.incdn with the corresponding occupations. The runsp lapw script will automatically copy the corresponding files to case.inc top of file: case.inc # of orbitals, shift of potential, print switch 1,-1,2 n (principal quantum number), kappa, occup. number 2,-1,2 2s 2,-2,4 2p 2, 1,2 2p* # of orbital of second atom 1,-1,2 1s 0 end switch bottom of file Interpretive comments on this file are as follows: line 1: free format nrorb, shift, iprint nrorb shift iprint number of core orbitals shift of potential for positive eigenvalues (e.g. for 4f states as core states in lanthanides) optional print switch to reduce (0) or increase (1) printing to case.outputc line 2: free format n, kappa, occup n principle quantum number kappa relativistic quantum number (see Table 6.6) occup occupation number (including spin), fractial occupations supported >>>: line 2 is repeated for each orbital (nrorb times; see line 1) >>>: line 1 and 2 are repeated for each inequivalent atom. Atoms without core states (e.g. H or Li) must still include a 1s orbital, but with occupation zero. line 3: free format

148 130 CHAPTER 7. SCF CYCLE 0 zero indicating end of job 7.11 MIXER (adding and mixing of charge densities) In mixer the electron densities of core, semi-core, and valence states are added to yield the total new (output) density (in some calculations only one or two types will exist). Proper normalization of the densities is checked and enforced (by adding a constant charge density in the interstitial). As it is well known, simply taking the new densities leads to instabilities in the iterative SCF process. Therefore it is necessary to stabilize the SCF cycle. In WIEN2k this is done by mixing the output density with the (old) input density to obtain the new density to be used in the next iteration. Several mixing schemes are implemented, but we mention only: 1. straight mixing as originally proposed by Pratt (52) with a mixing factor Q ρ new (r) = (1 Q)ρ old (r) + Qρ output (r) 2. a Multi-Secant mixing scheme contributed by L. Marks (see Marks and Luke 2008), in which all the expansion coefficients of the density from several preceding iterations (usually 6-10) are utilized to calculate an optimal mixing fraction for each coefficient in each iteration. It is very robust and stable (works nicely also for magnetic systems with 3d or 4f states at EF, only for ill-conditioned single-atom calculations you can break it) and usually converges at least 30 % faster than the old BROYD scheme. 3. Two new variants on the Multi-Secant method including a rank-one update (see Marks 2013) which appear to be 5-10% faster and equally robust. At the outset of a new calculation (for any changed computational parameter such as k-mesh, matrix size, lattice constant etc.), any existing case.broydx files must be deleted (since the iterative history which they contain refers to a different incompatible calculation). If the file case.clmsum old can not be found by mixer, a PRATT-mixing with mixing factor (greed) 1.0 is done. Note: a case.clmval file must always be present, since the LM values and the K-vectors are read from this file. The total energy and the atomic forces are computed in mixer by reading the case.scf file and adding the various contributions computed in preceding steps of the last iteration. Therefore case.scf must not contain a certain iteration-number more than once and the number of iterations in the scf file must not be greater than 999. For LDA+U calculations case.dmatup/dn and for onsite-hybrid-dft (switch -eece) case.vorbup/dn files will be included in the mixing procedure. With the new mode MSR1a (or MSECa) (contributed by L. Marks) atomic positions will also be mixed and thus optimized. This scheme can (unfortunately not in all cases) be a facter or 2-3 faster then the traditional optimization using min lapw Execution The program mixer is executed by invoking the command: mixer mixer.def or x mixer [-eece] A spin-polarized case will be detected automatically by x due to the presence of a case.clmvalup file. For an example see fccni (sec. 10.2) in the WIEN2k package.

149 7.11. MIXER Dimensioning parameters The following parameters are collected in file param.inc, : NCOM NRAD NSYM traptouch number of LM terms in density number of radial mesh points order of point group minimum acceptable distance between atoms in full optimization model Input Below a sample input (written automatically by lstart) is provided for T io 2 (rutile), one of the test cases provided with the WIEN2k package top of file: case.inm MSR1 0.d0 YES (PRATT/MSEC1/3/MSR1/a bg charge (+1 for additional e), NORM 0.2 MIXING GREED Not used, retained for compatibility only nbroyd nuse ## VLSOW, SLOW, FAST bottom of file Interpretive comments on this file are as follows: line 1: (A5,*) switch, bgch, norm switch MSEC1 Multi-Secant scheme (Marks and Luke 2008) MSEC2 similar to MSEC1 (above), but mixes the higher LM values inside spheres by an adaptive PRATT scheme. This leads to a significant reduction of programsize and filesize (case.broyd*) for unitcells with many atoms and low symmetry (factor 10-50) with only slighly worse mixing performance. MSEC3 Similar to MSEC1, but with updated scaling, regularization and other improvements. MSEC4 similar to MSEC3 (above), but mixes only the L=0 LM value MSR1 Recommended. A Rank-One Multisecant that is slightly faster than MSEC3 in most cases. For MSR1a see later. MSR2 similar to MSR1 (above), but mixes only the L=0 LM value MSR1a Similar to MSR1, but in addition it optimizes the atomic positions simultaneously (see Sect ) PRATT Pratt scheme with a fixed greed PRAT0 Pratt scheme with a greed restrained by previous improvement, similar to MSEC3 bgch Background charge to apply to the cell (e.g. use +1 if the system contains an additional electron or -1 to screen a core hole if it is not neutralized by an additional valence electron) norm YES Charge densities are normalized to sum of Z NO Charge densities are not normalized line 2: free format

150 132 CHAPTER 7. SCF CYCLE greed mixing greed Q. Essential for Pratt, rather less important for MSEC1. In the first iteration using Broyden s scheme: Q is automatically reduced by the program depending on the average charge distance :DIS andthe relative improvement in the last cycle. In case that the scf cycle fails due to large charge fluctuations, this can be further reduced but this can lead to stagnation. One should rarely reduce this below line 3 (optional): (free format) f pw, f clm f pw Not used, retained for input compatibility. f clm Not used, retained for input compatibility. line 4 (optional): (free format) nbroyd, nuse nbroyd Not used, retained for input compatibility. nuse For all Multisecant methods: Only nuse steps are used during modified broyden (this value has some influence on the optimal convergence. Usually 6-10 seems reasonable and 8 is the default). line 5 (optional line): (free format) trust VSLOW For very difficult cases, where divergence (like spin-polarized systems or with many TM atoms) or endless oszillations occur. SLOW FAST For easy cases to accelarate (also MSR1a). In addition, mixer reads a mixing factor from file.pratt or.msec, which can be used during scf/msr1a optimizations or at the very beginning to push convergence. You can create it using echo 0.2 >.pratt These files will be removed automatically once they are used. For additional documentation consult the README file in SRC mixer.

151 8 Programs for analysis, calculation of properties, and geometry optimization Contents 8.1 AIM BerryPI BROADENING DIPAN ELAST FILTVEC FSGEN IRelast IRREP JOINT KRAM LAPW LAPW LAPW MINI NMR OPTIC OPTIMIZE QTL SPAGHETTI TELNES TETRA XSPEC AIM (atoms in molecules) This program was contributed by: 133

152 134 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION Javier D. Fuhr and Jorge O. Sofo Instituto Balseiro and Centro Atomico Bariloche S. C. de Bariloche - Rio Negro, Argentina and Please make comments or report problems with this program to the WIEN-mailinglist. we will communicate the problem to the authors. If necessary, This program analyses the topology of the electron density according to Bader s Atoms in molecules theory. For more information see Bader 2001 and Sofo and Fuhr The original code has been significantly speeded-up by L.Marks There are some new optional keywords in the input (usually not needed, more for testing) and also more debugging output. All changes are described in $WIENROOT/SRC aim/notes.txt. Basically it performs two different tasks, namely searching for critical points (CP) and/or determination of the atomic basins with an integration of the respective charge density. It is important that you provide a good charge density, i.e. one which is well converged with respect to LMMAX in the CLM-expansion (you may have to increase the default LM-list to LM=8 or 10) and with as little core-leakage as possible (see lstart, sect. 6.4), otherwise discontinuities appear at the sphere boundary Execution The program aim is executed by invoking the command: aim aim.def or aimc aim.def or x aim [-c ] Dimensioning parameters The following parameters are listed in file param.inc: LMAX2 NRAD NSYM highest L in in LM expansion of charge and potential number of radial mesh points order of point group Input The input file contains SWITCHES, followed by the necessary parameters until an END-switch has been reached. Examples for critical-point searches and charge-integration are given below: top of file: case.inaim CRIT 1 # index of the atom (counting multiplicity) ALL # TWO/THRE/ALL /FOUR # x,y,z nshells (of unit cells) END bottom of file Interpretive comments on this file are as follows:

153 8.1. AIM 135 line 1: A4 CRIT Keyword to calculate critical points line 2: free format iatom index of the atom from where the search should be started. This count includes the multiplicity, i.e. if the first atom has MULT=2, the second atom has iatom=3 (Do not use simply the atom-numbers from case.struct) line 3: A4 KEY TWO, THRE, ALL, or FOUR defines the starting point for the CP search to be in the middle of 2, 3 or 4 atoms. ALL combines option TWO and THRE together. line 4: free format nxsh, nysh, nzsh specifies the number of nearest neighbor cells (in x,y,z direction) where atomic positions are generated. lines 1-4 can be repeated with different atoms or KEYs line 5: A4 END specifies end of job. In case.outputaim the critical points are marked with a label :PC :PC a1 a2 a3 l1 l2 l3 c lap rho iat1 dist1 iat2 dist2 where a1,a2,a3 are the coordinates of the CP in lattice vectors; l1 l2 l3 are the eigenvalues of the Hessian at the CP; c is the character of the CP (-3, -1, 1 or 3); lap is the Laplacian of the density at the CP (lap=l1+l2+l3) and rho is the density at the CP (all in atomic units). In case of a bond critical point (c=-1) also the nearest distances (dist1, dist2) to the two nearest atoms (iat1, iat2) are given. For convenience run extractaim lapw case.outputaim (see ) and get in the file critical points ang a comprehensive list of the CP (sorted and unique) with all values given in Å, e/å 3,... (instead of bohr) top of file: case.inaim SURF 3 atom in center of surface (including MULT) theta, 40 points, from zero to pi phi step along gradient line, rmin, check initial R for search, step (a.u) nshell IRHO "INTEGRATE" rho WEIT WEIT (surface weights from case.surf), NOWEIT radial points outside min(rmin,rmt) END bottom of file Interpretive comments on this file are as follows: line 1: A4

154 136 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION SURF Keyword to calculate the Bader surface. line 2: free format iatom index of the atom from where the search should be started. This count includes the multiplicity, i.e. if the first atom has MULT=2, the second atom has iatom=3 (Do not use simply the atom-numbers from case.struct) line 3: free format ntheta, thmin, thmax ntheta number of theta directions for the surface determination. This (and nphi) determines the accuracy (and computing time). thmin starting angle for theta thmax ending angle for theta. If you have higher symmetry, you can change the angles thmin=0, thmax=π and use only the irreducible part, i.e. when you have a mirror plane normal to z (see case.outputs), restrict thmax to π/2. line 4: free format nphi, phimin, phimax line 5: free format h0, frmin, nstep line 6: free format r0, dr0 line 7: free format nxsh, nysh, nzsh line 8: A4 nphi number of phi directions for the surface determination phimin starting angle phimax ending angle. (see comments for theta to reduce phi from the full 0 2π integration). h0 step in real space to follow the gradient ( 0.1) frmin defines the radius, for which the routine assumes that the search path has entered an atom, given as rmin = frmin * rmt ( ) nstep number of steps between testing the position being inside or outside of the surface ( 2-8). r0 initial radius for the search of the surface radius ( 1.5) dr0 step for the search of the surface radius( 0.1) specifies the number of nearest neighbor cells (in x,y,z direction) where atomic positions are generated. IRHO integrate function on unit 9 (usually case.clmsum) inside previously defined surface (stored in case.surf).

155 8.2. BERRYPI 137 line 9: A4 WEIT specifies the use of weights in case.surf. line 9: free format npt specifies number of points for radial integration outside the MT ( 30) line 8: A4 END specifies end of job. 8.2 BerryPI (Modern theory of polarization) This program was contributed by: S.J. Ahmed, J. Kivinen, B. Zaporzan, L. Curiel, S. Pichardo, O. Rubel Thunder Bay Regional Research Institute, Ontario, Canada Computer Physics Communications 184, (2013) Sources available from: https://github.com/spichardo/berrypi Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. This program calculates the spontaneous polarization, Born effective charges or piezoelectric constants using the Berry phase approach. More details about its usage are given in Chapter 5.8. It consists of a set of Python scripts (requires Python 2.7 and the NumPi library) and uses wien2wannier for the calculation of overlap integrals. The main steps of a berrypi -knx:ny:nz call include: x kgen -fbz generate a k-mesh in the full Brillouin zone write inwf Prepare the input for w2w with the occupied band range write win case Create the input file for w2w win2nnkp.py case Generate the nearest neighbor list of k-points x lapw1 Calculate wavefunctions for the new k-list x w2w Calculate the overlap matrix S mn (k j, k j+1 ) x lapwso and x w2waddsp (only in case of SO) mmn2pathphase.py case x Calculate the Berry phase along x-axis

156 138 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION 8.3 BROADENING (apply broadening to calculated spectra) This program was contributed by: Joachim Luitz IAST Austria Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. The broadening program can be used in conjunction with the TELNES3 or the xspec program to broaden theoretical spectra by applying a lorentzian broadening for core and valence life times and a gaussian broadening for spectrometer broadening Execution Execution The program broadening is executed by invoking the command: broadening broadening.def or x broadening Input broadening needs one input file - case.inb. When running TELNES3 this input file is automatically created from settings given in case.innes. GaN ELNES dummy

157 8.4. DIPAN 139 line value explanation 1 GaN... Title (of no consequence for the calculation) 2 ELNES ABS EMIS Type of input spectrum 3 NC C1 C2 specification of input file: NC number of columns to read, C1 and C2 column to broaden (only in ELNES mode) 4 SPLIT XINT1 XINT2 split energy, XINT1 2 relative intensities of spectra in C1 and C2 5 GA GB core hole lifetime of the two edges 6 W WSHIFT W: type of valence broadening (1: linear with E/10, 2: Muller like E 2 ), edge offset 7 S Spectrometer broadening FWHM in ev 8 dummy dummy keyword for compatibility with lorentz 9-11 E0, E1, E2 quadratic energy dependent broadening (only used for type ELNES and EMIS when selecting valence broadening type W=2) 8.4 DIPAN (Dipolar anisotropies) This program was contributed by: P. Novák Inst. of Physics, Acad.Science, Prague, Czeck Republic Please make comments or report problems with this program to the WIEN-mailinglist. we will communicate the problem to the authors. If necessary, This program calculates the magnetic dipolar hyperfine field and the dipolar magnetocrystalline anisotropy by a direct lattice summation over the magnetic moments of all sites. According to Wikipedia B = µ 0µ [3( nˆr)ˆr n] (8.1) 4πr3 where ˆr = r/r. n = M/M is direction of magnetization. µ 0 is permeability of free space; µ 0 = 4π10 7 H/m. B is the dipolar field in T. µ is magnetic dipolar moment in Am 2 = J/T, assumed to be parallel to n. r is in m. We want to express µ in Bohr magnetons µ B = J/T and r in atomic units for length a 0 (Bohr radius) a 0 = m. Inserting in (1) gives B = µ(µ B) 3 [3( nˆr)ˆr n]. (8.2) r(a.u.) Total dipolar field acting on atom i is given by the lattice sum B i = j µ j rj 3 [3( n ˆr j ) ˆr j n]. (8.3)

158 140 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION Dipolar anisotropy energy is given by the sum E an = 1 2V B j µ j (8.4) j when the sum is over atoms in the unit cell, V is the unit cell volume, Factor 1/2 appears because of the double summation. Expressing B j in T, µ j in µ B and V in (a.u.) 3 gives E an (J/m 3 ) = V (a.u.) 3 B j (T) µ j (µ B ) (8.5) j Execution The program dipan is executed by invoking the command: dipan dipan.def or x dipan Dimensioning parameters The following parameters are listed in files dipan.f: NATO NDIF number of inequivalent atoms in unit cell total number of atoms in unit cell Input An example is given below: top of file: case.indipan Rmax (a.u.), ipr (printing option) Magnetic moment of 1s atom (Y) in mu_b Magnetic moment of 2nd atom (Co(2c)) Magnetic moments of 3rd atom (Co(3g)) in mu_b Volume in a.u.**(-3) 2 ndir: numder of magnetization directions first direction for the magnetization second direction bottom of file Interpretive comments on this file are as follows: line 1: free format Rmax, IPR Rmax max distance (bohr) for lattice summation. Vary it for convergence check. IPR Print switch. IPR=2 produces very large files case.outputdipan and case.nn dipan line 2: free format mm Magnetic moment (µ B ) of first atom

159 8.5. ELAST 141 line 2 must be repeated for every non-equivalent atom in the unit cell line 3: free format VOLUME Unit cell volume in bohr**3 (grep :VOL case.scf) line 4: free format NDIR number of magnetization directions for which the dipolar contributions will be calculated. For NDIR > 1 the differences E an (dir i ) E an (dir j ) are also calculated. line 5: free format h,k,l direction of magnetization line 5 must be repeated NDIR times 8.5 ELAST (Elastic constants for cubic cases) This program was contributed by: original author: Thomas Charpin Lab. Geomateriaux de l IPGP, Paris, France (In September 2001 we received the sad notice that Thomas Charpin died in a car accident). modified by Ferenc Karsai Institute for MaterialsChemistry TU Vienna Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. This package calculates elastic constants for cubic crystals. It is described in detail by the author in Charpin Execution The package is driven by three scripts: init elast: It prepares the whole calculation and should be run in a directory with a valid case.struct and case.inst file. It creates the necessary subdirectories elast, elast/eos, elast/tetra, elast/rhomb, elast/result, the templates for tetragonal and rhombohedral distortion and initializes the calculations using init lapw. elast setup: It should be run in the elast directory, generates the distorted struct-files and eos.job, rhomb.job and tetra.job. These scripts must be adapted to your needs (spinpolarization, convergence,...) and run. elast setup can be run several times (for different distortions,...).

160 142 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION ana elast: Once all calculations are done, change into elastresult and run this script. The final results are stored in elastresultoutputs. genetempl, setelast, anaelast: These three small programs are called by the above scripts. The following modifications of init elast, elast setup and ana elast prepare input files for calculations of elastic constants at different pressures and analyze the results: init elast pressure: As in the case of init elast the script is called in the working directory with a valid case.struct file and requires an input file case.inelastp1 (a template can be found at $WIENROOT/SRC templates/template.inelastp1). The script creates the directory elast/ with the necessary subdirectories pressure x/ according to the number x of pressure changes in the case.inelastp1 input file and the templates for isotropic, tetragonal and rhombohedral (trigonal) distortions at each pressure (pressure 1/eos, pressure 1/tetra, pressure 1/rhomb, pressure 2/eos,...). In each pressure x/ directory a file called z pressure.dat is created with the lattice constant at each pressure given in case.inelastp1. In contrast to init elast the calculations are initialized using init lapw in batch mode and the necessary parameters are set in case.inelastp1. The following small programs and scripts are utilized by init elast pressure: iniel pressure reader.pl, iniel pressure in2reader.pl, genetempl elast setup pressure: Similar to elast setup this script has to be run in the elast directory and requires the input file elast.inelastp2 (a template can be found at $WIENROOT/SRC templates/elast.inelastp2). It creates the distorted struct files and the pressure x/eos.job, pressure x/rhomb.job, pressure x/tetra.job and pressure x/runjob.x files in each directory pressure x. The three scripts eos.job, rhomb.job and tetra.job can either be started separately or together by runjob.x. The number of structure changes per pressure and the calculational parameters are set in elast.inelastp2. The following small programs and scripts are utilized by elast setup pressure: elast setup input.pl, setelast pressure ana elast pressure: Once all calculations are done, this script (in contrast to ana elast) has to be run in the elast directory. It requires the pressure x/z pressure.dat files created by init elast pressure. The final results for a given pressure are stored in pressure x/elast/result/outputs. Additionally the collective results for all pressure are stored in the directory elast results. If the script is called with the option plot (eg. ana elast pressure --plot) then postscript files for the fits using gnuplot are created in the pressure x/results/outputs directory. The following small programs and scripts are utilized by ana elast pressure: anaelast pressure Input Below are examples for case.inelastp1 and elast.inelastp2: top of file: case.inelastp RMT_reduction XC_PBE V_xc_potential -6 CORE_separation 9 RKMAX NUMBER_of_k-points 15 GMAX NM SPIN NM INST bottom of file

161 8.5. ELAST 143 Interpretive comments on this file are as follows: line 1: free format RMT RMT reduction by X % OLD RMT values taken from case.struct file in working directory line 2: free format V xc Exchange-correlation potential line 3: free format E sep Energy seperation for core and valence states line 4: free format RKMAX RKMAX value line 5: free format k-mesh Number of k-points in full BZ line 6: free format GMAX GMAX value line 7: free format SPIN NM non magnetic SPIN spin polarized line 8: free format INST OLD case.inst file is taken from working directory NEW new case.inst file is created line 9: Empty line line 10-x: free format a, p a p lattice constant in a.u. at pressure p (determined from e.g. a previous volume optimization...) pressure p written in pressure x/z pressure.dat The elast.inelastp2 file looks like: top of file: elast.inelastp iso 0 tet 0 trig

162 144 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION 2 ec spin.false. parallel.true bottom of file Interpretive comments on this file are as follows: line 1-3 (optional): free format distortion, n distortion if this line is given then the specified distortions will be calculated iso isotropic distortion tet tetragonal distortion trig trigonal(rhombohedral) distortion n number of structure changes n for a given type of distortion; the exact changes in the lattice constant are given on the following n lines (free format, lines 4-8 in the example above) 0 default values are taken ( 10%, 9%,..., 1%,0%,1%,...,9%,10% - 21 values) > 0 change in the lattice constant in % line 9 (optional): free format ec energy convergence criterion (if this line is missing then default value of is used) line 10 (optional): free format spin.false. no spin polarization (default).true. spin polarization (runsp lapw used instead of run lapw in eos.job, tetra.job and rhomb.job) line 11 (optional): free format parallel.false. default.true. if.machines exists in the elast/ directory then it will be copied into pressure x/eos, pressure x/tetra, pressure x/rhomb directories

163 8.6. FILTVEC FILTVEC (wave function filter / reduction of case.vector) This program was contributed by: Uwe Birkenheuer Max-Planck-Institut für Physik komplexer Systeme Nöthnitzer Str. 38, D Dresden, Germany and Birgit Adolph University of Toronto, T.O., Canada Please make comments or report problems with this program to the WIEN-mailinglist. we will communicate the problem to the authors. If necessary, The program filtvec reduces the information stored in case.vector files by filtering out a user-specified selection of wave functions. Either a fixed set of band indices can be selected which is used for all selected k-points (global selection mode), or the band indices can be selected individually for each selected k-point (individual selection mode). The complete wave function and band structure information for the selected k-points and bands is transferred to case.vectorf. The information on all other wave functions in the original file is discarded. The structure of the generated case.vectorf file is identical to that of the original case.vector file. Hence, it should be possible to use case.vectorf as substitutes for case.vector anywhere in the WIEN program package. (This has only been tested for lapw7.and filtvec.) To filter vector files from spinpolarized calculations, filtvec has to be run separately for both the spin-up and the spin-down files. filtvec has not yet been adapted for w2web Execution The program filtvec is executed by invoking the command: filtvec filtvec.def or filtvecc filtvec.def or x filtvec [-c] [-up dn] [-hf] In accordance with the file handling for lapw1 and lapw7 the input vector file case.vector is assumed to be located in the WIEN scratch directory, while the reduced output vector file case.vectorf is written to the current working directory. See filtvec.def for details Dimensioning parameters The following parameters are listed in file param.inc (r/c): NKPT LMAX LOMAX number of k-points maximum number of L values used (as in lapw1) maximum L value used for local orbitals (as in lapw1) The parameter LMAX and LOMAX must be set precisely as in lapw1; all other parameters must not be chosen smaller than the corresponding parameters in lapw1.

164 146 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION Input Two examples are given below. The first uses global selection mode; the second individual selection mode. I. Global Selection Mode top of file # number of k-points, k-points # number of bands, band indices end of file Interpretive comments on this file are as follows. line 1: line 2: free format kmax ik(1)... ik(kmax) free format nmax ie(1)... ie(nmax) Number of k-point list items, followed by the list items themselves. Positive list items mean selection of the k-point with the specified index; negative list items mean selection of a range of k-points with indices running from the previous list item to the absolute value of the current one. E.g. the sequence 2-5 stands for 2, 3, 4, and 5. Number of band index items, followed by the list items themselves. Again, positive list items mean selection of a single band index; negative list items mean selection of a range of band indices. II. Individual Selection Mode top of file : # number of k-points # k-point, number of bands, band indices # k-point, number of bands, band indices end of file Interpretive comments on this file are as follows. line 1: line 2: free format kmax free format ik nmax ie(1)... ie(nmax) the number of individual k-points to be selected. This number must be followed by any text, e.g. SELEC- TIONS or simply :, to indicate individual selection mode. First the index of the selected k-point, then the number of band index items, followed by the list items for the current k-point themselves. Positive list items mean selection of the band with the specified index; negative list items mean selection of a range of band indices running from the previous list item to the absolute value of the current one. E.g. the sequence 3-7 stands for 3, 4, 5, and 7. This input line has to be repeated kmax-times.

165 8.7. FSGEN FSGEN (Fermi-surface generation) Unfortunately there is no really versatile tool for Fermi surface generation or analyzing FS properties. We have collected here a series of small programs together with some description on how to proceed to generate 2D-Fermisurfaces within WIEN. As usually, you have to run an scf cycle and determine a good Fermi-energy. Good means here a Fermi-energy coming from a calculation with a dense k-mesh. You should than create a mesh within a plane of the BZ, where you want to plot the FS. Some utility programs like sc fs mesh, (fcc, bcc, cxz mon and hex are also available) may help you here, but only some planes of the BZ have been implemented so far. Please check these simple programs and modify them according to your needs. Copy the generated k-mesh fort.2 to case.klist. Run lapw1 with this k-mesh. Run spaghetti with input-options such that it prints the bands which intersect EF to case.spaghetti ene (line 10, see sec. 8.20) Edit case.spaghetti ene and insert a line at the top: NX, NY, x-len, y-len, NXinter, NYinter, Invers, Flip where NX, NY are the number of points in the two directions x-len, y-len are the length of the two directions of the plane (in bohr 1, you can find this in case.spaghetti ene) NXinter, NYinter: interpolated mesh, e.g. 2*NX-1 Invers: 0/1: mirrors x,y FLIP: 0/1: flips x,y to y,x Run spagh2rho < case.spaghetti ene to convert from this format into a format which is compatible with the case.rho file used for charge density plotting. It generates files fort.11, fort.12,... (for each band separately) and you should use your favorite plotting program to generate a contourplot of the FS (by using a contourlevel = 0). Alternatively you can use for plotting: Run fsgen lapw 11 xx save filename, which is a small shell script that can plot all fermi surfaces using the data-files fort.11, fort.12,... fort.xx generated in the previous steps. It requires the public domain package pgplot and the contour-plot program plotgenc. (The latter can be obtained from unsupported/, but you must have installed the pgplot library before.) 8.8 IRelast (Elastic constants for cubic, hexagonal, tetragonal, orthorhombic, monoclinic and rhombohedral cases) This program was contributed by: author: Morteza Jamal Ghods City-Tehran, Iran m Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. This package calculates elastic constants for cubic, hexagonal, orthorhombic, tetragonal, monoclinic and rhombohedral symmetry, respectively. It replaces previous versions on our unsupported software page.

166 148 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION The package is driven by the following scripts: set elast lapw: It prepares the whole calculation and should be run in a directory with a valid case.struct file. It finds the symmetry (S= C(cubic), H(hexagonal), T(tetragonal), O(orthorhombic), M(monoclinic) or R(rhombohedral) of the structure defined in case.struct and calls S set elast lapw. It creates the necessary subdirectories elast-constant, elast-constant/c11, elast-constant/c22,... and copies information of the present working directory into those new directories. command init lapw gets information to produce auto init lapw for automatic initialization. Then it gets the options for running the scf-cycle in the job files using S command run lapw. Finally, it generates the distorted structfiles and symm.job files, where symm stands for CUBIC, HEX, TETRA, ORTHO, MONO, and RHOM, using the S setupc11, S setupc22,... programs.. modifyjob lapw: allows you to edit and modify the previously created symm.job files. This step is not necessary when you have specified proper commandline options previously. calljob lapw : will execute all produced job files in elast-constant/c11/case, elast-constant/c22/case,... sequentially, but eventually you may run all those jobs by yourself on different machines in parallel, as these steps can take quite some time. Once all calculations are done: cal elast lapw: calls all S ana elast lapw and S ana elastc lapw scripts and determines the elastic constants C ij as well as the Voigt, Reuss, Hill, Bulk, Shear and Young modulus and the Poisson ratio (using data from the auxiliary program S InverseELC). Using data from the auxilliary programs S InverseELC and MassRho, S ana elast lapw calculate the Sound Velocity and the Debye temperature. The main output files are case.output elastic and INVELC-matrix, which contains the elastic compliance constants (invers of the elastic constants matrix). Finally, S ana elastorder lapw will check the sensitivity of the results to the order of the polynomial fit (stored in file output-order) and, for monoclinic crystals, the TWS program which transforms the elastic constants from WIEN2k to STANDARD Cartesian coordinates (in file STDELC-matrix). When you know your symmetry, you can simply call the corresponding series of scripts (S = C, H, T, O, M or R): S set elast lapw S modifyjob lapw S calljob lapw S ana elast lapw After a first run you may check your results using more datapoints (more or different displacements). This can be done conveniently by S setupcxx, where XX = 11, 12,..., which should be run in the corresponding elast-constant/cxx/case directory. When you specify in addition to new datapoints also your old displacements, these old results will be automatically taken into account in the analysis without recalculating them. On the other hand, when you want to change some computational parameters (RKmax, k- mesh, XC-potential) you can call command init lapw after S setupcxx and then modify your symm.job file specifying set answscf=no and a modified savename (eg. pbe rkm8). After these preparations, you can rerun symm.job and S ana elast lapw and check if your elastic constants are converged with respect to computational parameters. Additional information can be found in $WIENROOT/SRC IRelast/guide.

167 8.10. JOINT IRREP (Determine irreducible representations) This program was contributed by: Clas Persson Condensed Matter Theory Group,Department of Physics, University of Uppsala, Sweden Please make comments or report problems with this program to the WIEN-mailinglist. we will communicate the problem to the authors. If necessary, This program determines the irreducible representation for each eigenvalue and all your k-points. It is in particular useful to analyse energy bands and their connectivity. You need a valid vector file, but no other input is required. The output can be found in case.outputir and case.irrep. For nonmagnetic SO calculations you must set IPR=1 in case.inso. The output of this program is needed when you want to draw bandstructures with connected lines (instead of dots ). It will not work in cases of non-symmorphic spacegroups AND k-points at the surface of the BZ. See also $WIENROOT/SRC irrep/readme Execution The program irrep is executed by invoking the command: irrep [up/dn]irrep.def or x irrep [-so -up/dn -hf] Dimensioning parameters The following parameters are listend in file param.inc: LOMAX max. no. of local orbital. should be consistent with lapw1 and lapwso NLOAT number of different types of LOs MSTP max. step to describe k as a fraction MAXDG max. no. of degenerate eigenfunctions MAXIRDG max. no. of degenerate irr. representations FLMAX size of flag (FL) array (should be 4) MAXIR max. no. of irreducible representations NSYM max. no. of symmetry operations TOLDG min. energy deviation of degenerate states, in units of Rydberg 8.10 JOINT (Joint Density of States) This program was contributed by:

168 150 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION Claudia Ambrosch-Draxl Atomistic Modelling and Design of Materials University Leoben A-8700 Leoben, AUSTRIA Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. This program carries out the BZ integration using the momentum matrix elements case.symmat calculated before by optic. The interband or the intraband contributions to the imaginary part of the dielectric tensor (ɛ 2 ) can be computed. Alternatively, the DOS or the joint DOS can be derived. The output in case.joint can be plotted with any xy-plotting package or opticplot lapw or Curve lapw. Warning: Negative values for ɛ 2 may occur due to negative weights in Blöchl s tetrahedron method. For optional XMCD calculations (see OPTICS) an integration of the Brillouin zone is carried out using the momentum matrix elements from case.symmat1up and case.symmat2up (if both edges are present, otherwise only from case.symmat1up). The broadened and unbroadened spectra are written in files case.xmcd and case.rawxmcd: in these files, the first coloumn is the energy mesh, the second and third coloumns the left and right polarized absorption spectra, the fourth column the XMCD and the last is the XAS. For L 2,3, M 2,3, and M 4,5 edges, the broadened and unbroadened spectra for the single edges (useful for the application of Carra s and Thole s sum rules) are stored in case.broad1 and case.broad2 and case.raw1 and case.raw2, respectively, where 1 and 2 are refererred to the higher and lower energy core state Execution The program joint is executed by invoking the command: joint joint.def or x joint [-up dn] [-hf] Dimensioning parameters The following parameter is listend in files param.inc: NSYM order of point group MG0 number of columns (usually 9) Input An example is given below: top of file: case.injoint : LOWER,UPPER,upper-valence BANDINDEX : EMIN DE EMAX FOR ENERGYGRID IN ryd ev : output units ev / ryd XMCD : omitt these 4 lines for non-xmcd : core energies in Ry (grep :2P case.scfc) : core-hole broadening (ev) for both core states 0.1 : spectrometer broadening (ev) 4 : SWITCH 2 : NUMBER OF COLUMNS

169 8.10. JOINT : BROADENING (FOR DRUDE MODEL - switch 6,7) bottom of file Interpretive comments on this file are as follows: line 1: free format b1, b2, b3 lower, upper and (optional) upper-valence band-index (Setting b3 may allow for additional analysis (restricting the occupied bands from b1- b3) and in big cases it will reduce memory requirements. Otherwise set b3 equal b2) line 2: free format emin, de, emax Energy window and increment in Ry (emin must not be negative) line 3: free format units ev output in units of ev Ry output in units of Ry line 4: optional line for XMCD, must be omitted for normal optic; free format XMCD keyword for XMCD calculation, requires 3 more lines line 4xmcd: must be omitted for normal optic; free format E core1, E core2 lower and higher core energies (in Ry, get them using eg. grep :2P case.scf ) line 4xmcd: must be omitted for normal optic; free format broad core1, broad core2 lifetime broadening (ev) of lower and higher core state line 4xmcd: must be omitted for normal optic; free format broad spectrometer (Gaussian) broadening (ev) line 4+: free format switch 0 joint DOS for each band combination 1 joint DOS as sum over all band combinations 2 DOS for each band 3 DOS as sum over all bands 4 imaginary part of the dielectric tensor (ɛ 2 ) 5 imaginary part of the dielectric tensor for each band combination 6 intraband contributions: number of free electrons per unit cell assuming bare electron mass (calculated around E F ± 10 de as defined in input line 4), plasma-frequency

170 152 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION 7 in addition to switch 6 the contributions from different bands to the plasma frequency are analyzed. line 5: free format ncol number of columns line 6: free format broadening x,y,z broadening parameters (in units defined in line 3) for Drude-model The band analysis for all options (switches 0, 2, 5, and 7) has been improved: For each tensor component additional files are created, where each column contains the contributions from a single band or band combination. The file names are e.g..im eps xx 1,.Im eps xx 2, or.jdos 1 etc. where the number of files depend on the number of bands/band combinations. Warning: The number of band combinations might be quite large! 8.11 KRAM (Kramers-Kronig transformation) This program was contributed by: Claudia Ambrosch-Draxl Atomistic Modelling and Design of Materials University Leoben A-8700 Leoben, AUSTRIA Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. The Kramers-Kronig analysis is carried out for the actual number of columns contained in the case.joint[up dn] file. For each real component its imaginary counterpart is created and vice versa. All dielectric tensor components can be found in file case.epsilon[up dn]. The real and imaginary parts of the optical conductivity (in /s) are written to file case.sigmak[up dn]. In addition, file case.absorp contains the real parts of the optical conductivity (in 1/(Ωcm) and the absorption coefficients. The loss function is also calculated (case.eloss), where for the previously calculated Plasma-frequency the intraband contributions can be added. Please note, that for spin-polarized calculations, the Kramers-Kronig analysis is NOT really additive, i.e. most quantities (like ɛ 1 ) cannot be obtained by simply adding the spin-up and dn results to get the total contribution (see equations in Ambrosch 06). Thus, one should add up both spin contributions of ɛ 2 (in case.jointup and case.jointdn) using addjoint-updn lapw (this will produce case.joint) before calling (non-spinpolarized) x kram. The 3 sumrules are also checked and written to case.sumrules. The output in case.epsilon[up dn] and case.sigmak[up dn] can be plotted with any xyplotting package, opticplot lapw or the OPTIC -task in w2web Execution The program kram is executed by invoking the command: kram kram.def or x kram [-up dn]

171 8.12. LAPW Dimensioning parameters The following parameters are listed in files param.inc: MAXDE maximum number of points in energy mesh MPOL fixed at Input An example is given below: top of file: case.inkram gamma for Lorentz broadening (in units selected in joint) 0.0 energy shift (scissors operator) (in units selected in joint) 1 add intraband contributions? yes/no: 1/ plasma frequencies (for each column in case.injoint) 0.20 Gammas for Drude terms (for each column in case.injoint) bottom of file Interpretive comments on this file are as follows: line 1: free format EGAMM Lorentz broadening (in energy units selected in joint) line 2: free format ESHIFT Energy shift (scissors operator) (in energy units selected in joint) line 3: free format INTRA 0 Intraband contributions are not added 1 Intraband contributions are added (requires plasma-frequencies calculated by joint using switch 6 ) ) line 4: free format EPL Plasma-frequencies (calculated by joint using SWITCH=6 for all columns) line 5: free format EDRU Broadening for Drude terms (for all columns) 8.12 LAPW3 (X-ray structure factors) This program calculates X-ray structure factors from the charge density by Fourier transformation. You have to specify interactively valence or total charge density (because of the different normalization of case.clmsum and case.clmval) and a maximum sinθ/λ value.

172 154 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION Execution The program lapw3 is executed by invoking the command: lapw3 lapw3.def or lapw3c lapw3.def or x lapw3 [-c ] Dimensioning parameters The following parameters are listend in file param.inc r or param.inc c : LMAX2 NCOM NRAD highest L in in LM expansion of charge and potential number of LM terms in density number of radial mesh points 8.13 LAPW5 (electron density plots) This program generates the charge density (or the potential) in a specified plane of the crystal on a two dimensional grid which can be used for plotting with an external contour line program of your choice. Depending on the input files one can generate valence (case.clmval) or difference densities (i.e. crystalline minus superposed atomic densities) using the additional file (case.sigma). In spinpolarized cases one can produce up-, dn- and total densities but also spin densities (difference up-dn). It is also possible to plot total densities (case.clmsum), Coulomb (case.vcoul), exchange-correlation (case.r2v) or total (case.vtotal) potentials, but in those cases the file lapw5.def has to be edited and you must replace case.clmval by the respective filename. The file case.rho contains in the first line npx, npy, xlength, ylength; and then the density (potential) written with: write(21,11) ((charge(i,j),j=1,npy),i=1,npx) 11 format(5e16.8) In order to get 3D-data for plotting with xcrysden, you can also use the script prepare xsf lapw (see Sect ). A recent extension by L.D. Marks allows to calculate STM immages (constant current) according to the Tersoff-Hamman approximation. Before doing this, you have to run lapw2 with a suitable energy window around the Fermi energy, which should correspond to the experimental bias voltage (x lapw2 -all EMIN EMAX. The output contains the z-position (height) of the tip, i.e. the position where the density has the specified value. It is strongly recommended that you use Run Programs Tasks Electron density plots from w2web, see the TiC example in Fig Execution The program lapw5 is executed by invoking the command: lapw5 lapw5.def or lapw5c lapw5.def or x lapw5 [-c -up dn]

173 8.13. LAPW Dimensioning parameters The following parameters are listend in file param.inc: LMAX2 NCOM NRAD NPT00 NSYM highest L in in LM expansion of charge and potential number of LM terms in density number of radial mesh points number of radial mesh points beyond RMT order of point group Input An example is given below. You may want to use XCRYSDEN by T.Kokalj to generate this file (see sect ) top of file: case.in # origin of plot: x,y,z,denominator # x-end of plot # y-end of plot # x,y,z nshells (of unit cells) # nx,ny RHO # RHO/DIFF/OVER; ADD/SUB or blank ANG VAL NODEBUG # ANG/ATU, VAL/TOT, DEBUG/NODEBUG NONORTHO # optional line: ORTHO NONORTHO GAUSS # this and the following lines are for STM mode # vibrational tensor STM 4.0D-5 3 # STM mode, density-level, axis (3=z-axis) SEMPER # optional output format for semper7 code FAST # optional, useful for a first crude check bottom of file Interpretive comments on this file are as follows: line 1: free format ix,iy,iz,idv The plane and section of the plot is specified by three points in the unit cell, an origin of the plot, an x-end and an y-end. The first line specifies the coordinates of the origin, where x=ix/idv,... in fractional units of the lattice vectors (except fc, bc and c lattices, where the lattice vectors of the conventional cell are used). Note the special meaning for STM mode described below. line 2: free format ix,iy,iz,idv coordinates of x-end line 3: free format ix,iy,iz,idv coordinates of y-end (The two directions x and y must be orthogonal to each other unless NONORTHO is selected). Since it is quite difficult to specify those 3 points for a rhombohedral lattice, an auxiliary program rhomb in5 is provided, which creates those points when you specify 3 atomic positions which will define your plane. You can find this program using Run Programs Other Goodies from w2web. The most convenient way to specify this plane (for a more complex structure) is using XCrysDen, where you can simply click on 3 atoms which will span the plane.

174 156 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION line 4: free format nxsh, nysh, nzsh specifies the number of nearest neighbor cells (in x,y,z direction) where atomic positions are generated (needs to be increased for very large plot sections, otherwise some atoms are not found in the plot) line 5: free format npx, npy specifies number of grid points in plot. npy=1 produces a file case.rho onedim containing the distance r (from the origin) and the respective density, which can be used in a standard x-y plotting program. line 6: format (2a4) switch, addsub switch RHO charge (or potential) plots, no atomic density is used (regular case) DIFF difference density plot (crystalline - superposed atomic densities), needs file case.sigma (which is generated with LSTART, see section 6.4) OVER superposition of atomic densities, needs file case.sigma addsub NO (or blank field): use only the file from unit 9 ADD adds densities from units 9 and 11 (if present), e.g. to add spin-up and down densities. SUB subtracts density of unit 11 (if present) from that of unit 9 (e.g. for the spin-density, which is the difference between spin-up and down densities). line 7: format (3a4) iunits, cnorm, debug iunits ATU density (potential) in atomic units e/a.u. 3 (or Ry) ANG density in e/å 3 (do not use this option for potentials) cnorm determines normalization factor VAL used for files case.clmval, r2v, vcoul, vtotal TOT used for files case.clmsum debug DEBU debugging information is printed (large output) line 8 (optional): free format noorth1 ORTHO (default) enforces directions to be orthogonal NONORTdirections can be arbitrary; use this option only if your plotting program supports non orthogonal plots (e.g. for XCRYSDENS). line 9 (this and the following lines are optional for the STM mode): free format VIBRATIONGAUSS suggested mode of vibrational smearing line 10: free format V11,V12,V22,V13,V23,V33 the size matrix components of the vibration tensor in units of distance squared, where the units are either ANG or ATU as defined earlier

175 8.14. LAPW7 157 line 11: free format MODE, level, axis MODE STM enables STM mode level the density level (typically e /ang 3 ). If this value is inappropriately chosen, the code will terminate with a statement: Cannot Bracket, sorry. axis the axis normal to the surface (e.g. 3 for z-axis). Note that in STM mode the z-coordinate specified in the first 3 lines is used as a starting value for the search of the z-position where the density has the value of level. This starting z-value has to be in the interstitial (vacuum) region. line 12 (optional): free format SEMPER this keyword puts the output in a format readable by the semper7 code (exchange of x,y order). line 13 (optional): free format FAST this keyword performs a fast approximate calculation for checking if your input (in particular the density level) is reasonable. In order to plot total densities or potentials (see cnorm as above) you have to create lapw5.def using x lapw5 -d, then edit lapw5.def and insert proper filenames (case.clmval, case.r2v, case.vcoul, case.vtotal) for units 9 and 11, and finally run lapw5 lapw5.def LAPW7 (wave functions on grids / plotting) This program was contributed by: Uwe Birkenheuer Max-Planck-Institut für Physik komplexer Systeme Nöthnitzer Str. 38, D Dresden, Germany and Birgit Adolph, University of Toronto, T.O., Canada Please make comments or report problems with this program to the WIEN-mailinglist. we will communicate the problem to the authors. If necessary, The program lapw7 generates wave function data on spatial grids for a given set of k-points and electronic bands. lapw7 uses the wave function information stored in case.vector (or in reduced (filtered) form in case.vectorf which can be obtained from case.vector by running the program filtvec). Depending on the options set in the input file case.in7(c) one can generate the real or imaginary part of the wave functions, it s modulus (absolute value) or argument, or the complex wave function itself. For scalar-relativistic calculations both the large and the small component of the wave functions can be generated (only one at a time). The wave functions are generated on a grid which is to be specified in the input file(s). The grid can either be

176 158 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION any arbitrary list of points (to be specified free-formatted in a separate file case.grid) or any n-dimensional grid (n = 0...3). The operating mode and grid parameters are specified in the input file case.in7(c). As output lapw7 writes the specified wave function data for further processing e.g. for plotting the wave functions with some graphical tools such as gnuplot in raw format to case.psink. For quick inspection, a subset of this data is echoed to the standard output file case.outputf (the amount of data can be controlled in the input). In case, lapw7 is called many times for one and the same wave function, program overhead can be reduced, by first storing the atomic augmentation coefficients A lm, B lm (and C lm ) to a binary file case.abc. For the spin-polarized case two different calculations have to be performed using either the spin-up or the spin-down wave function data as input. It should be easy to run lapw7 in parallel mode, and/or to apply it to wave function data obtained by a spin-orbit interaction calculation. None of these options have been implemented so far. Also, lapw7 has not yet been adapted for w2web. Please note: lapw7 requires an LAPW basis set and does not work with APW+lo yet Execution The program lapw7 is executed by invoking the command: lapw7 lapw7.def or lapw7c lapw7.def or x lapw7 [-c] [-up dn] [-sel] [-hf] With the -sel option lapw7 expects data from the reduced (filtered) wave function file case.vectorf, otherwise the standard wave function file case.vector is used. The reduced vector file case.vectorf is assumed to resist in the current working directory, while the standard vector file case.vector (which may become quite large) is looked for in the WIEN scratch directory. For details see lapw7.def Dimensioning parameters The following parameters are listed in file param.inc (r/c): NRAD NSYM LMAX7 LOMAX number of radial mesh points order of point group maximum L value used for plane wave augmentation maximum L value used for local orbitals The meaning of LMAX7 is the same as that of LMAX2 in lapw2 and that of LMAX-1 in lapw1. Rather than being an upper bound it directly defines the number of augmentation functions to be used. It may be set different to LMAX2 in lapw2 or LMAX-1 in lapw1, but it must not exceed the latter one. Note that, the degree of continuity of the wave functions across the boundary of the muffin tin sphere is quite sensitive to the choice of the parameter LMAX7. A value of 8 for LMAX7 turned out to be a good compromise Input A sample input is given below. It shows how to plot a set of wave functions on a 2-dim. grid top of file D ORTHO # mode O(RTHOGONAL) N(ON-ORTHOGONAL) # x, y, z, divisor of origin # x, y, z, divisor of x-end # x, y, z, divisor of y-end

177 8.14. LAPW # grid points and echo increments NO # DEP(HASING) NO (POST-PROCESSING) RE ANG LARGE # switch ANG ATU AU LARGE SMALL 1 0 # k-point, band index bottom of file Interpretive comments on this file are as follows. line 1: A3,A1 mode flag mode the type of grid to be used ANY An arbitrary list of grid points is used 0D,1D,2D or 3D An n-dim. grid of points is used. n = 0, 1, 2, or 3. flag orthogonality checking flag (for n-dim. grids only) N The axes of the n-dim. grid are allowed to be non-orthogonal. O or The axes of the n-dim. grid have to be mutual orthogonal. blank line 2: free format (for n-dim. grids only) ix iy iz idiv Coordinates of origin of the grid, where x=ix/idv etc. in units of the conventional lattice vectors. line 3: free format (for n-dim. grids with n > 0 only) ix iy iz idiv Coordinates of the end points of each grid axis. This input line has to be repeated n-times. line 4: free format (not for 0-dim. grids) np... npo... In case of an n-dim. grid, first the number of grid points along each axis, and then the increments for the output echo for each axis. Zero increments means that only the first and last point on each axis are taken. In case of an arbitrary list of grid points, the total number of grid points and the increment for the output echo. Again a zero increments means that only the first and last grid point are taken. Hence, for n-dim. grids, altogether, 2 n integers must be provided; for arbitrary lists of grid points two intergers are expected. line 5: format(a3) tool DEP NO post-processing of the wave functions Each wave function is multiplied by a complex phase factor to align it (as most as possible) along the real axis (the so-called DEP(hasing) option). No post-processing is applied to the wave functions. line 6: format(a3,1x,a3,1x,a5) switch iunit whpsi switch RE IM the type of wave function data to generate The real part of the wave functions is evaluated. The imaginary part of the wave functions is evaluated.

178 160 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION iunit whpsi ABS ARG PSI ANG AU or ATU The absolute value of the wave functions is evaluated. The argument the wave functions in the complex plane is evaluated. The complex wave functions are evaluated. the physical units for wave function output Å units are used for the wave functions. Atomic units are used for the wave functions. the relativistic component to be evaluated LARGE The large relativistic component of wave function is evaluated. SMALL The small relativistic component of wave function is evaluated. line 7: free format iskpt iseig iskpt iseig The k-points for which wave functions are to be evaluated. Even if the wave function information is read from case.vectorf, iskpt refers to the index of the k-point in the original case.vector file! If iskpt is set to zero, all k-points in case.vector(f) are considered. The band index for which wave functions are to be evaluated. Even if the wave function information is read from case.vectorf, iseig refers to the band index in the original case.vector file! If iseig is set to zero, all bands (for the selected k-point(s)) which can found in case.vector(f) are considered. line 8: format(a4) this line is optional handle augmentation coefficient control flag SAVE or Augmentation coefficients are stored in case.abc). No wave function data is generated in this case. This option is only allowed if a single STOR(E) wave function is selected in the previous input line. READ Previously stored augmentation coefficients are read in (from or case.abc). This option is only allowed if the same single wave function as the one who s augmentation coefficients are stored in case.abc REPL(OT) is selected in the previous input line. anythingaugmentation coefficients are generated from the wave function information else in case.vector(f) MINI (Geometry minimization) This program is usually called from the script min lapw and performs movements of the atomic positions according to the calculated forces (please read Sec ). It generates a new case.struct file which can be used in the next geometry/time step. Depending on the input options, mini helps to find the equilibrium positions of the atoms or performs a molecular dynamics simulation (which might take very long time). For finding the equilibrium positions different methods are available. We recommend PORT, a reverse-communication trust-region Quasi-Newton method from the Port library (http: //www.bell-labs.com/project/port/doc/port3doc.tar.gz, Gay 1983), which was implemented by L.D.Marks edu). It minimizes the total energy and NOT the forces (using the forces as derivative of E vs. atomic positions). In cases when energy and forces are not compatible, eg. because of numerical noise due to limited scf convergence, small RKmax or crude k-mesh, PORT may fail. An interesting alternative is a sophisticated modified steepest-descent method (NEW1), which minimizes the

179 8.15. MINI 161 forces (does not use the total energy). Eventually a damped Newton dynamics is also available. The forces are read from a file case.finm, while the history of the geometry optimization or MD is stored in case.tmpm One can constrain individual positions in case.inm or define linear constrains for several positions using case.constraint (thanks to B.Yanchitsky (Kiev, for details see comments in the SRC templates/template.constraint file). In case of calculations with linear constrains one should use NEW1 (in case.inm). When constraining individual positions and using PORT, one should after modifications in case.inm rerun x pairhess -copy (which copies.minpair to.minrestart and.min hess) Execution The program mini is executed by invoking the command: mini mini.def or x mini Dimensioning parameters The following dimensioning parameters are collected in the file param.inc: MAXIT NRAD NCOM NNN NSYM maximum number of geometry steps number of radial mesh points number of LM terms in density number of neighboring atoms for nn order of pointgroup Input Two examples are given below; one for a PORT geometry optimization, and one for molecular dynamics using a NOSE thermostat: Input for geometry optimization: top of file: xxx.inm PORT (PORT/NEWT tolf step0 (a4,2f5.2)) ( 1..3:delta, 4:BO/eta(1=friction zero)) ( 1..3=0 constraint) bottom of file Interpretive comments on this file are as follows. line 1: format(a4,2f5.2) MINMOD Modus of the calculation PORT Geometry optimization with reverse-communication trust-region Quasi-Newton routine from the Port library. Recommended option. NEW1 Performs geometry optimization with sophisticated steepest-descent method with automatic adaptation of stepsize (still experimental, but when PORT fails, an interesting alternative) NEWT Performs geometry optimization with damped Newton scheme according to

180 162 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION TOLF STEP0 BFGS R τ+1 m = Rm τ + η m (Rm τ Rm τ 1 ) + δ m Fm τ where Rm τ and Fm τ are the coordinate and force at time step τ. When the force has changed its direction from the last to the present timestep (or is within the tolerance TOLF), η m will be set to 1 η m. Please see also the comments in Sect Performs geometry optimization with the variable metric method of BFGS. This option works only when a quadratic approximation is a good approximation to the specific potential surface. Obsolete. Force tolerance, geometry optimization will stop when all forces are below TOLF. Initial Trust-region radius. Determines size of first geometry step. line 2: free format DELTA(1-3) ETA For PORT (and BFGS): Precondition parameters: rescales the gradient and thus determines the size of the geometry steps For NEWT/NEW1: x,y,z-delta parameters. Determines speed of motion. Good values must be found for each individual system. They depend on the atomic mass, the vibrational frequencies and the starting point (see Sect ). DELTA(i) = 0 constrains the corresponding i-th coordinate (for PORT: after setting a DELTA(i)=0, also rerun pairhess to set a proper Hessian). The delta-x,y,z correspond to the global coordinates (the same as the positions in case.struct and the forces :FGL from case.scf). Whenever you change these DELTA(i) you must remove file case.tmpm! For NEWT: damping (friction) parameter. ETA=1 means no friction, ETA=0 means no speed from previous time steps PORT: changes the strength of the bonds when running pairhess and ZWEIGHT is negative (see the pairhess description), otherwise not used NEW1: ETA is not used >>> line 2: must be repeated for every atom Input for Molecular dynamics: top of file: nbc.inm NOSE (NOSE/MOLD (a4)) (Masse, delta t, T, nose-frequency) bottom of file Interpretive comments on this file are as follows. line 1: format(a4,f5.2) MINMOD MOLD NOSE Modus of the calculation Performs next molecular dynamics timestep Performs next molecular dynamics timestep using a NOSE thermostat line 2: free format

181 8.16. NMR 163 MASS TIMESTEP Atomic mass of i th atom Time step of MD (in atomic units, depends on highest vibrational frequencies) TEMP Simulation Temperature (K) NOSF Nose-frequency >>>line 2: must be repeated for every atom 8.16 NMR (chemical shielding) This program was contributed by: Robert Laskowski Inst.Materials Chemistry TU Vienna A-1060 Vienna, AUSTRIA Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. This program calculates the orbital contribution to the NMR (chemical) shielding (the total shielding for insulators). It will first calculate the perturbation of the wave functions due to the magnetic field (first order perturbation theory) and the resulting current. This induced current is then integrated (via the Biot-Savart law) to obtain the magnetic shielding at a nucleus. For details see Laskowski,Blaha 2012, 2012a, 2013, 2014). The program does not need to be called by the user, but it is interfaced with the script x nmr lapw (all details can be found in sect. 5.6), where the different modes/options can be selected as switches. It can run in k-point as well as in mpi-parallel mode. It does not have its own input file, but a modified case.in1 is necessary, which needs to be generated by x nmr lapw -mode in1. We need an extended basis set with several local orbitals (up to very high energies) for all l + 1 states, where l refers to the maximal chemical l of the specific atom (l=1 for C, but 2 for Fe,..). In addition ALL eigenvalues must be calculated, which increases the cpu-time of lapw1 as compared to a normal scf-calculation. In addition lapw1/2 and nmr is run for 7 different k-meshes, an unshifted one as well as plus/minus shifted meshes in x, y and z direction OPTIC (calculating optical properties) This program was contributed by:

182 164 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION Claudia Ambrosch-Draxl Atomistic Modelling and Design of Materials University Leoben A-8700 Leoben, AUSTRIA Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. The theoretical background is described in detail in Ref. Abt 1994 and Ambrosch-Draxl 06 (Please cite the latter when publishing optics results!). The calculation of optical properties requires a dense mesh of eigenvalues and the corresponding eigenvectors. For that purpose start kgen and generate a fine k-mesh (with many k-points). Run lapw1 and then lapw2 with the option FERMI (Note: You must also put TETRA / with value=101. for metallic systems case.in2) in order to generate the weight-file. After the vector-file has been generated by lapw1 run optic in order to produce the momentum matrix elements. Then the program joint carries out the BZ integration and computes the imaginary part of the complex dielectric tensor. In order to obtain the real part of the dielectric tensor kram may be executed which uses the Kramers-Kronig relations. The program optic generates the symmetrized squared momentum matrix elements M i =< n k p. e i n k > 2 between all band combinations for each k-point given in the vector-file and stores them in case.symmat. For the orthogonal lattices the squared diagonal components can be found in the file case.mat diag. For non-orthogonal systems all 6 components (M j ) M k can be calculated according to the symmetry of the crystal. In systems without inversion symmetry the complex version opticc must be executed. The matrix elements (and the imaginary part of the dielectric tensor) are given per spin in case of the spin-polarized calculation and as a sum of both spin directions if the calculation is nonspinpolarized. Due to spin-orbit coupling imaginary parts of the nondiagonal elements may occur in spinpolarized cases. Thus in general, up to 9 components can be calculated at the same time. Since version WIEN2k 11.1 an option for the calculation of XMCD (X-ray magnetic circular dichroism) has been added by Lorenzo Pardini Please cite Pardini et al when using XMCD and check the paper for further details. In the case of the XMCD calculation, the momentum matrix elements in the dipole approximation between the selected core state and conduction states are stored in case.symmat1up (higher energy core state, eg. L 3 ) and case.symmat2up (lower energy core state, eg. L 1 ) for each k-point and every band. For K, L 1, and M 1 edges, only case.symmat1up is written, since in these cases there is only one edge, whereas both case.symmat1up and case.symmat2up are written for the remaining cases. XMCD calculation can be only performed for system with spin-polarized AND spin-orbit set up. In order to calculate XMCD and x-ray absorption spectra, eigenvalues must be evaluated over a mesh in the whole Brillouin zone; for that porpouse, the following procedure should be followed: copy case.struct to case.ksym (cp case.struct case.ksym) and remove all the symmetry operations but the identity; generate a k-mesh in the whole Brilouin zone (x kgen -so); change TOT to FERMI in case.in2c; set IPRINT=1 in case.inc to activate core-wavefunction output; for metallic systems, put TETRA with value 101; execute runsp lapw -so -s lapw1 -e lcore;

183 8.17. OPTIC 165 run optic: x optic -c -so -up; run joint: x joint -up. You must not use p-1/2 relativistic LOs in LAPWSO, since this basis is not supported on OPTICS yet Execution The program optic is executed by invoking the command: optic(c) optic.def or x optic [-c -up dn -so -p -hf] Recommended procedure for spin-orbit coupling: In order to get the correct matrix elements, the files case.vectorso[up dn] have to be used. For that purpose the following procedure is recommended: run SCF cycle: run[sp] lapw -so generate a fine k-mesh for the optics part: x kgen [-so (if case.ksym has been created by symmetso) ] change TOT to FERMI in case.in2c execute run[sp] lapw -so -s lapw1 -e lcore with this fine k-mesh run optic: x opticc -so [-up] run joint: x joint [-up] run kram: x kram [-up] In cases of non-spinpolarized spin-orbit calculations WITHOUT inversion symmetry one must do some tricks and mimick a spinpolarized calculation: cp case.vsp case.vspup cp case.vsp case.vspdn cp case.vectorso case.vectorsoup x lapw2 -fermi -so -c cp case.weight case.weightup cp case.weight case.weightdn x optic -so -up x joint -up Due to the paramagnetic weight files (which are normalized to 2 electrons per band instead of one) all your results (joint/sigma...) must be divided by a factor of two. Note: In spin-polarized cases with spin-orbit only one call to optic, joint and/or kram (either up or down) is necessary, since the spins are not independent any more and both vector-files are used at the same time Dimensioning parameters The following dimensioning parameters (listed in param.inc r and param.inc c) are used: LMAX LOMAX NRAD NSYM highest l+1 in basis function inside sphere (reducing LMAX to 4 or 5 may dramatically speed-up optics for large cases, but of course the matrix elements will be truncated and do not have full precision) highest l for local orbital basis (consistent with input in case.in1) number of radial mesh points order of point group

184 166 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION Input An example is given below: top of file: case.inop : NKMAX, NKFIRST : EMIN, EMAX, NBvalMAX XMCD 1 L23 : optional line: for XMCD of 1st atom and L23 spectrum 2 : number of choices (columns in *symmat) 1 : Re xx 3 : Re zz OFF : ON/OFF writes MME to unit bottom of file Interpretive comments on this file are as follows: line 1: free format nkmax, nkfirst maximal number of k-points, number of k-point to start calculation line 2: free format emin, emax absolute energy range (Ry) for which matrix elements should be calculated nbvalmax optional input. Setting this to the number of occupied bands (see case.output2) will reduce cpu-time of optics (for large cases, MM only between occupied and empty bands) line 3: optional line, must be omitted for normal optic; free format XMCD fixed keyword to indicate XMCD calculation. You should also use NCOL=6 natom atom number (from case.struct file) for which XMCD should be calculated edge specify the edge: must be K, L1, L23, M1, M23 or M45 line 3+: free format ncol number of choices (columns in case.symmat) line 4+: free format icol column to select. Choices are: 1... Re < x >< x > 2... Re < y >< y > 3... Re < z >< z > 4... Re < x >< y > 5... Re < x >< z > 6... Re < y >< z > 7... Im < x >< y > 8... Im < x >< z > 9... Im < y >< z > Options 7-9 apply only in presence of SO, options 4-6 only in nonorthogonal cases.

185 8.18. OPTIMIZE 167 line 5: free format IMME, NATOMS (optional input) IMME NATOMS OFF/ON; optionally prints unsquared momentum matrix elements to unit 4 number of atoms for which the opt. matrix elements should be calculated (The index of the atoms is read in the next line). Please note, that since we need the squared matrix elements, the sum of ɛ 2 using atom 1 and atom 2 separately is NOT the same as using atom 1 and 2 together, since we miss crossterms. Nevertheless this can be a useful option to analyze the origin of certain peaks in ɛ 2. I recommend to repeat this analysis for all possible combinations, and also for a list of all atoms, since this shows the effect of the interstitial (and crossterms involving the interstitial). line 6: (optional) free format IATOMS List of NATOMS atoms for which the opt. matrix elements should be calculated (see above) OPTIMIZE (Volume, c/a or 2-4 dimensional lattice parameter optimization) This program generates a series of new struct files corresponding to different volumes, c/a ratios, or otherwise different lattice parameters (depending on your input choice) from an existing struct file (either case initial.struct or case.struct). (When case initial.struct is not present, it will be generated from the original case.struct. Furthermore it produces a shell script optimize.job. You may modify this script and execute it. Further analysis of the results (at present only equilibrium volume or c/a ratio are supported in w2web) allows to find the corresponding equillibrium parameters (see Sec.5.3.1) Execution The program optimize is executed by invoking the command: optimize optimize.def or x optimize Input You have to specify interactively which task should be performed (volume, c/a, b/a optimization, or full optimization for tetragonal, orthorhombic or monoclinic structure), how many cases you want to do and how large the change (+/- xx %) should be for each case QTL (calculates special partial charges and population matrices) This program was contributed by:

186 168 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION P. Novák and J.Kuneš Inst. of Physics, Acad.Science, Prague, Czeck Republic Please make comments or report problems with this program to the WIEN-mailinglist. we will communicate the problem to the authors. If necessary, qtl creates the input for calculating total and projected density of states of selected atoms (with a limit of 28 different atoms) and selected l-subshells. It thus provides similar data as lapw2 -qtl, but it allows for additional options. In particular it supports calculation of DOS projected on relativistic states p 1/2, p 3/2, d 3/2, d 5/2, f 5/2, f 7/2, DOS projected on states in a rotated coordinate system and DOS projected on individual f states. qtl also allows to calculate population matrix and energy resolved population matrix. Comparing to lapwdm population matrix, the matrix created by qtl may contain also the cross terms between different orbital and spin numbers and it can be energy resolved. Important option of the qtl is the symmetrization that makes the calculation longer, but must be switched on whenever the quantities, which are not invariant are calculated. Detailed description may be found in QTL - technical report by P. Novák. The calculation is based on the spectral decomposition of a density matrix on a given atomic site and its transformation to the required basis. The output is written to case.qtl [up/dn]. For the DOS calculation the file case.qtltext [up/dn] is created in which the ordering of partial charges is given. Please note, that in contrast to case.qtl [up/dn] from x lapw2 -qtl the total partial charge of an atom is NOT multiplied with its multiplicity and contains only the sum of the requested l,m terms (eg. s,p,d) and thus not all contributions. Also the interstital charge will usually be NOT correct Execution The program qtl is executed by invoking the command: x qtl [ -up/dn -so -p -hf] or qtl qtl.def Input A sample input (a default is created automatically during init lapw for case.inq is given below top of file: case.inq Emin Emax 2 number of selected atoms iatom1 qsplit1 symmetrize loro nl1 p d iatom2 qsplit2 symmetrize loro nl2 s p d f new axis z bottom of file Interpretive comments on this file are as follows:

187 8.19. QTL 169 Table 8.93: Possible values of QSPLIT and their interpretation QSPLIT meaning -2 DOS in basis according to ISPLIT from case.struct -1 DOS in relativistic j, l, s, m j > basis 0 DOS in relativistic j, l, s, m j > basis, summed over m j 1 DOS in l, m l > basis (no symmetry) 2 DOS in basis of real orbitals (no symmetry) 3 axial symmetry 4 hexagonal symmetry 5 cubic symmetry 6 user written unitary transformation 88 population matrix, no < l l > crossterms corresponds to ISPLIT=88 99 full population matrix including < l l > crossterms (as ISPLIT=99) line 1: free format emin,emax energy window line 2: free format natom number of atoms selected for calculation (max. 28, if more are needed you have to run qtl in junks ) line 3: free format iatom, QSPLIT, symmetrize, loro iatom QSPLIT symmetrize loro line 4: free format Nl(iatom), (l(iatom,i),i=1,nl(iatom)) Nl l line 5: free format hz, kz, lz integer, index of atom integer, analog of ISPLIT in case.struct: see below integer, =0 (no symmetrization), 1 (symmetrization) integer =0 original coord. system preserved =1 (new z axis) =2 (new z and x axes) number of orbital numbers selected for calculation orbital numbers selected for calculation for atom iatom real*8, direction of new axis z (if loro=1,2) Lines starting from line 3 are repeated for each selected atom. Line 5 only appears when calculation in new coordinate system is required (loro 0). Axis z in this system is along hz,kz,lz (in units of the lattice vectors, need not be normalized). If not only the z axis, but also the x axis need to be specified, then loro must be equal to 2 and additional line hx, kx, lx (real*8) giving the direction of the new axis x, perpendicular to the new axis z must appear. For relativistic splitting (QSPLIT=0,-1) this rotation is ignored and z points along the direction of magnetization as defined in case.inso. Indices of selected atoms, as well as the orbital numbers, must form an ascending sequence. For QSPLIT=6 (unitary transformation prepared by user) the unitary matrices are read as in WIEN2k 07 qtl: For the i-th atom selected for qtl calculation, they are stored in case.cf$i and ordered according to increasing l. The unitary transformation matrix must rotate from the standard lms -basis to the desired one. A few examples (e.g. jjz, lms, or e g t 2g ) are supplied with

188 170 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION the code in $WIENROOT/SRC templates/template.cf * and must be copied to case.cf$i. For less common cases these must be generated by hand Output The results in file case.qtl[up/dn] are written in the same format as lapw2 file case.qtl[up/dn] and thus they may be directly used by tetra. The data for the interstital DOS correspond to n = nat + 1 (nat is number of atom types). The ordering of densities for all selected atoms is summarized in the file case.qtltext[up/dn]. The qtltext file that corresponds to the input data given above is: Ordering of DOS in QTL file for: HoMnO3 (Munoz) atom 1 ordering of projected DOS p,px,py,pz, real basis d,dz2,d(x2-y2),dxy,dxz,dyz, real basis atom 3 ordering of projected DOS s p,pxy,pz, axial basis d,dz2,d(x2-y2),d(yz+xz),dxy, axial basis f,a2,[x(t1)+y(t1)],z(t1),[ksi(t2)+eta(t2)],zeta(t2), axial basis A2=xyz x(t1)=x(x2-3r2/5) y(t1)=y(y2-3r2/5) z(t1)=z(z2-3r2/5) ksi(t2)=x(y2-z2) eta(t2)=y(z2-y2) zeta(t2)=z(x2-y2) Data for interstital DOS correspond to atom index 8 The output for the population matrix integrated over energy is written to case.dmat [up/dn] that has the same format as analogous file calculated by lapwdm SPAGHETTI (energy bandstructure plots) This program generates an energy bandstructure plot (postscript file case.spaghetti ps and xmgrace file case.bands.agr) using the eigenvalues printed in case.output1 or case.outputso (with switch -so) or case.energy (with switch -enefile). Using the SCF potentials one runs x lapw1 -band with a special k-mesh (case.klist band) along some high-symmetry lines (some sample inputs can be found in SRC templates/*.klist or you create your own k-mesh using Xcrysden). As an option, one can emphasize the character of the bands by additionally supplying corresponding partial charges (file case.qtl which can be obtained using x lapw2 -qtl -band, see 7.7). This will be called band-character plotting below, in which each energy is drawn by a circle whose radius is proportional to the specified character of that state. It allows to analyze the character of bands (see also figures 3.12 and 3.13). The file case.bands.agr can be opened directly with xmgrace. Within xmgrace, all features of the plot, such as the plot range, the plot size, line properties (style, thickness and color), axis properties, labels, etc. can easily be changed by either using the menu (submenus of the Plot menu) or double-klicking on the corresponding part of the figure. The size of the characters for a band-character plot can be changed in the menu Plot / Graph appearance / Z normalization. The figures can directly be printed or exported in eps, jpg, png and other formats, via the menus File / Print setup and File / Print.

189 8.20. SPAGHETTI 171 C.Persson has modified this program and it allows now also to draw connected lines. For this purpose it uses the irreducible representations (from file case.irrep produced by program irrep together with a table of compatibility relations to decide which points should be connected (non-crossing rule!). (Note: This option will NOT work on the surface of the BZ for non-symmorphic spacegroups, because the corresponding group-theory has not been implemented.) The presence of incompatible case.irrep or case.qtl files (from a previous run or qtls from a DOS calculation) may crash spaghetti. In such cases it is necessary to remove these files explicitly. It is strongly recommended that you use Run Programs Tasks Bandstructure from w2web Execution The program spaghetti is executed by invoking the command: spaghetti spaghetti.def or x spaghetti [-up dn] [-so] [-p] [-hf] [-enefile] The -p switch directs spaghetti to use the case.output1 * files of a k-point parallel lapw Input An example is given below: top of file: case.insp ### Figure configuration # paper offset of plot # xsize,ysize [cm] # major ticks, minor ticks # character height, font switch # line width, line switch, color switch ### Data configuration # energy range, energy switch (1:Ry, 2:eV) # Fermi switch, Fermi-level (in Ry units) # number of bands for heavier plotting 1, # jatom, jtype, size of heavier plotting bottom of file Interpretive comments on this file are as follows: line 1: free format test test line must start with ###. Begin of figure description. This tests also if you use the new input (different from WIEN97 or early WIEN2k versions) line 2: free format xoffset, yoffset xoffset yoffset x offset (in cm) of origin of plot y offset (in cm) of origin of plot line 3: free format xsize,ysize xsize plotsize in x direction (cm)

190 172 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION ysize plotsize in y direction (cm) line 4: free format eincr, mtick eincr mtick energy increment where y-axis labels are printed (major ticks) number of minor ticks of y-axis line 5: free format charh, font charh scaling factor for size of labels font 0 no text 1 Times and Symbol 2 Times,Times-Italic and Symbol 3 Helvetica, Symbol, and Helvetica-Italic 4 include your own fonts in defins.f line 6: free format linew, ilin, icol linew line width ilin 0 dots or open circles 1 lines 2 lines and open circles 3 lines and filled circles icol 0 black 1 one-color plot 2 three-color plot 3 multi-color plot 4 multi-color plot,one color for each irred. representation line 7: free format test test line must start with ###. Begin of data description. line 8: free format emin, emax, iunits emin emax iunits energy minimum of plot energy maximum of plot 1 energies in Ry (internal scale) 2 energies in ev with respect to E f line 9: free format iferm, efermi iferm 0 no line at EF 1 solid line at EF 2 dashed line at EF 3 dotted line at EF

191 8.21. TELNES3 173 efermi Fermi energy (Ry); can be found in the respective case.scf file. If set to 999., E f is not plotted (and iunits=2 cannot be used) line 10: free format nband1, nband2 lower and upper band index for bands which should show bandcharacter plotting (if case.qtl is present and the proper switch is set, see below). In addition the corresponding x and y coordinates are written to file case.spaghetti ene (which can be used for plotting with an external xy-plotting program). line 11: free format jatom, jcol, jsize jatom jcol jsize If a case.qtl file is present, jatom indicates the atom whose character (selected by jcol) is used for band-character plotting (dots are replaced by circles with radii proportional to the corresponding weight, requires ilin=0,2,3). If set to zero or if case.qtl is not present, bandcharacter plotting does not occur. specifies the column to be used in the respective QTL-file. 1 means total, 2... s, 3... p,... The further assignment depends on the value of ISPLIT set in case.struct. (ignored for jatom=0). The description can be found in the header of case.qtl. size factor for radii of circles used in band-character plotting if line 11 is repeated, one can average the QTLs for different atoms (but with identical jcol and jsize) TELNES3 (calculation of energy loss near edge structure) This program was contributed by: Kevin Jorissen and Cécile Hébert Ecole Polytechnique Federale de Lausanne Please make comments or report problems with this program to the WIEN-mailinglist. we will communicate the problem to the authors. If necessary, The TELNES3 program calculates the double differential scattering cross section (DDSCS) on a grid of energy loss values and impulse transfer vectors. This double differential cross section is integrated to yield a differential cross section, which is written to file. The differential cross section is either a function of energy (ELNES integrated over impulse transfer q); or a function of impulse transfer (ELNES integrated over energy loss E), which shows the angular behavior of scattering. The DDSCS is calculated as described in a forthcoming publication by K. Jorissen, C. Hebert, and J. Luitz. (The Ph.D. thesis of K. Jorissen (http://www.wien2k.at/reg_user/textbooks/) also describes the formalism onto which TELNES3 is built in great detail.) This formalism allows calculation of relativistic EELS including transitions of arbitrary order (i.e., non-dipole transitions). It takes into account the relative orientation between sample and beam. If this is not

192 174 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION necessary (because the crystal is isotropic, or the sample is polycrystalline), the formula may be integrated over 4π, simplifying the calculation. Both scenarios are implemented in TELNES3. A note to our faithful fans from the early days: it used to be necessary to play such tricks as recompiling lapw2 with lxdos=3 ; to create k-meshes without symmetry ; and to edit case.struct and set ISPLIT to 99. This is no longer necessary. Just sit back, relax, and press the buttons in w2web. The integration with the package qtl will do the job Execution Execution The program telnes3 is executed by invoking the command: telnes3 telnes3.def or x telnes3 [-up -dn] Input TELNES3 requires one input file - case.innes. We recommend using InnesGen TM of w2web to create this input file in a clear and intuitive way. If you wish to manually edit the file, please refer to the following description. Please note that input files created for TELNES2 may or may not work with TELNES3, depending on which optional keywords were used. There isn t a shred of compatibility with the old TELNES program. The file case.innes consists of two parts: a first block with required input, and a second block with optional input. In fact, the second part may be omitted altogether. The simplest input file looks like this: Graphite C K edge of first atom. 1 (atom) 1, 0 (n, l core) 285 (E-Loss of 1st edge in ev) 300 (energy of the incident electrons in kev) (the energy mesh) (collection semiangle, convergence semiangle, both in mrad) 10 1 (NR, NT, defining the integration mesh in the detector plane) 0.8 (spectrometer broadening in ev) END This first part of the file is not formatted and contains the following information:

193 8.21. TELNES3 175 line value explanation 1 Graphite... Title (of no consequence for the calculation) 2 1 Atom number as given in case.struct (the index which numbers inequivalent atoms) main and orbital quantum number n and l of the core state; eg. 1 0 stands for 1 s energy of the edge onset in ev (here for the C K edge) beam energy in kev energy mesh given as E min E max E step ; all values in ev. 0.0 is the edge threshold detector collection semiangle and microscope convergence semiangle in mrad parameters NR and NT which determine the mesh used for sampling the distribution of Q-vectors allowed by collection and convergence angles spectrometer broadening FWHM in ev 10 END keyword telling the program that there is no more input to read. Optional keywords and values must be inserted before this line! There are many other parameters that control the calculation, most of which are set to reasonable default values. To use these advanced parameters, add corresponding keywords before the END keyword. We recommend using InnesGen TM of w2web to create this input file. Currently, the keywords listed below may be used. Although only the first four characters of each keyword are read, we recommend using the full keyword for clarity. VERBOSITY n eg. : 1 Specifies how much output you ll get. n must be 0 (only basic output; default), 1 (medium output) or 2 (full output, including more technical information). ATOMS n1 n2 eg. : 1 3 (default : 1 0 == 1 mult(natom) ) The atom number on line 2 (see above) corresponds to a class of equivalent atoms in case.struct. Equivalent positions n1 to n2 will contribute to the spectrum (default : sum over all atoms in the equivalency class). Since all equivalent atoms have identical electronic structure up to a symmetry operation, this will simply yield a prefactor (n2-n1+1) for the orientation averaged spectrum, but as each equivalent atom has a different orientation with respect to the beam, this setting will influence the shape of an orientation sensitive spectrum. DETECTOR POSITION theta_x theta_y eg. : (default : 0 0) By default, the detector is aligned with the incoming beam - i.e., source, sample, and detector are connected by a straight line. This card shifts the detector in a plane perpendicular to the incoming beam. The shift is expressed as an angle in mrad. If one draws a line between source and sample, and another line from the sample to the center of the detector aperture, these 2 lines will form an angle of theta 2 x + theta 2 y mrad. MODUS m eg. : angles (default is energy)

194 176 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION The output is a spectrum as a function of energy if m=energy. The output is a spectrum as a function of impulse transfer/scattering angle if m=angle. SPLIT splitting energy eg. : 2.7 If the initial state has an orbital quantum number larger than 0, it will generate two superposed edges: one corresponding to j = l 1/2, and one corresponding to j = l + 1/2 (eg., for the 2p initial state we have a L3 and a L2 edge). The splitting energy sets the energy separation of the two edges and should be given in ev (here, L3 is at the energy specified in the beginning of case.innes, and L2 is 2.7 ev higher). By default (keyword omitted), the splitting energy is calculated by the program. It is generally quite accurate. BRANCHING RATIO branching ratio eg. : 1.4 The branching ratio is a scaling factor (eg., here the ratio of intensities L3/L2 would be set to 1.4). By default (keyword omitted), the branching ratio is set to its statistical value of (2l + 2)/2l. NONRELATIVISTIC This key tells the program not to use the relativistic corrections to the scattering cross section. This option generates spectra identical to output of the old TELNES program. This produces incorrect results in many cases. By default, relativistic calculations are done. INITIALIZATION make_dos write_dos eg. N N (default : Y Y) make_rot.mat. write_rot.mat eg. Y N (default : Y Y) TELNES3 needs many ingredients for its calculations, and this key defines how it gets two of them: the density of states, and the rotation matrices (used for transforming q-vectors from one atom to an equivalent atom). The first entry says whether or not the ingredient has to be calculated (Y : calculate; N : read from file), and the second entry says whether or not the ingredient has to be written to file (Y : write; N : don t write). If make dos=y, a file case.qtl must be present from which the dos will be calculated. If make dos=n, then either a file case.dos or a file case.xdos containing the (x)dos must exist. If make rot.mat=n, a file case.rotij containg the rotation matrices must exist. If write rot.mat=y, a file case.rotij is written. If write dos=y, a file case.dos or case.xdos is written. The calculation of the rotation matrices is computationally negligible, but it is recommended to write the xdos to file and not calculate it over and over again. QGRID qmodus eg. L (U by default) theta_0 eg (no default value) ) A collection angle α and convergence angle β allow scattering angles up to α + β and a corresponding set of Q-vectors. This set (a disk of radius α + β) is sampled using a discrete mesh. Three types of meshes are implemented : U a uniform grid, where each Q-vector samples an equally large part of the disk. Sampling is set up by drawing NR equidistant circles inside the big circle, and choosing (2i 1)NT points on circle i, giving NR 2 NT points in total.

195 8.21. TELNES3 177 L a logarithmic grid with NR circles. The distance between circles increases exponentially. There are (2i 1)NT points on circle i, and NR 2 NT points in total. Circle i is at radius theta 0 e ((i 1)dx), where dx depends on NR, α and β. 1 a one dimensional logarithmic mesh; there are NR circles at exponential positions, and only one point on each circle (so NR points in total). This means we sample a line in the detector*beam plane. An economic way of getting spectra as a function of scattering angle in cases with symmetric scattering. The line specifying theta 0 is to be omitted for the U grid. ORIENTATION SENSITIVE g1 g2 g3 (eg ) (no default value) This key tells the program not to average over sample to beam orientations, but to use the particular sample to beam orientation defined by the three Euler angles (to be given in degrees). The Euler angles (0,0,0) means that the electron beam is parallel to the c-axis of the crystal and the 3 angles rotate with respect to the x-, y- and z-axes, respectively. Most likely, this option needs larger NR (and NT). If the ORIENTATION SENSITIVE key is not set, the program will average over all orientations (default). SELECTION RULE type (eg. : q) (default : n) The formula for the DDSCS contains an exponential factor in q, which we expand using the Rayleigh expansion. We identify each term in the expansion by the order lambda of the spherical Bessel function j λ (q) it contains. This key keeps some terms and discards others. This can be useful to eliminate unwanted transitions ; to study a spectrum in greater detail ; or simply to speed up the calculation significantly. Possible settings for type are : m : use lambda = 0 only d : use lambda = 1 only q : use lambda = 2 only o : use lambda = 3 only n : no selection rule, calculate all transitions 0-3 : all transitions up to lambda (eg., 1 means lambda = 0 and 1) Be aware that the availability of the DOS limits the possible transitions (WIEN2k gives us the DOS only up to l=3). In the nonrelativistic limit, the SELECTION RULE and LSELECTION RULE coincide i.e., the λ = 1 terms correspond to dipole transitions etc. This is no longer true in the relativistic case. LSELECTION RULE type (eg. : q) (default : d) Whereas the previous key selects transitions by the order of the interaction potential, this key selects them by the L-character of the final states. Possible settings for type are (the orbital momentum of the initial state being denoted with l): m : L=l d : L=l +/- 1 q : L=l +/- 2 o : L=l +/- 3 n : no selection rule, calculate all transitions 0-3 : L-l <= type

196 178 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION Be aware that the availability of the DOS limits the possible transitions (WIEN2k gives us the DOS only up to l=3). In the nonrelativistic limit, the SELECTION RULE and LSELECTION RULE coincide i.e., the λ = 1 terms correspond to dipole transitions etc. This is no longer true in the relativistic case. EXTEND POTENTIALS Rmax sampling lmax refine (e.g.: ) (no defaults) Calculate matrix elements beyond the muffin tin radius up to r = rmax (in Bohr units). Refine the radial grid by a factor refine (1 means default sampling density). This is done by evaluating the potential as given in case.vtotal, which must be present for this type of calculation, and reexpanding it in spherical harmonics, using an angular grid with step of sampling degrees, and expanding up to l=lmax. Currently, users should keep lmax to 0 and almost certainly refine to 1.0. However, advanced users can play around with the software and tweak it to do interesting things if they wish. TELNES3 only requires the spherical potential l=0. FERMI ENERGY Ef (e.g. 0.75) Manually set the Fermi energy to Ef (needs to be given in Rydberg units). (The default behavior is to get Ef from the header of case.qtl.) CORE WAVEFUNCTION filename (e.g. case.cwf) Read the wave function of the initial state from file. (Default behavior is to calculate it instead.) FINAL STATE WAVEFUNCTION filename (e.g. case.finalwf) Read the radial wave functions of the final state from file. (Default behavior is to calculate it instead.) RELATIVISTIC Itype (e.g. 1) Determines which flavor of relativity to use : 0 means nonrelativistic (as in TELNES), 1 means fully relativistic (default), 2 means using the contracted q-vector (only valid for dipole transitions ; as in TELNES2). NOHEADERS Don t put headers in output files. This can be helpful if your plotting program doesn t like the headers. (Gnuplot doesn t mind them.) DOSONLY Don t calculate the EELS spectrum halt the program after the calculation of the density of states is finished. NBTOT nb (e.g. 200 )

197 8.21. TELNES3 179 Arrays for the DOS are first allocated at some initial size, and then reallocated at larger size if necessary. Unfortunately, these reallocation routines appear unstable in some circumstances. This card allows the user to set an array size manually and avoid the need to reallocate (nb is the number of bands). However, very large systems may lead the system to run out of memory and cause a crash. The following cards are not yet activated (placeholders): TABULATE, SPIN The following cards are no longer active and must be removed or renamed: XQTL, WRONG Practical considerations A typical ELNES calculation consists of the following steps: initialize (init lapw) and converge a SCF calculation (run lapw) provide a suitable case.innes file if more excited states are needed than given by the SCF calculation, raise the upper energy limit in case.in1 and run x lapw1 create the case.qtl file using x qtl -telnes calculate the EELS spectrum using x telnes3. It is generally a smart move to make the program calculate the DOS on the biggest energy grid you wiill ever need, save this to file, and simply read it from file for all future calculations (INITIALIZATION key). The same should be done for calculations using EXTEND POTENTIAL (use CORE WAVEFUNCTION key to save to file). This saves time. (In case of disk space problems, once the case.qtl file has been created, the case.vector files can be deleted. Similar, the case.qtl file can be deleted or compressed once the case.dos file exists.) add broadening to the spectrum using x broadening. If you wish, editing the case.inb file allows tweaking of the broadening. study the output (case.elnes or case.broadspec are the place to start). if you wish to do more calculations, save the current results using save eels -d calculation1. Edit case.innes and run x telnes3 again. This sequence can conveniently be executed using w2web by simply clicking one button after the other Files TELNES3 uses a lot of files. Many output files are only written if VERBOSITY is set to a high level. Many input files are required only for certain input settings in case.innes. We list here all files possibly used by TELNES3 (and listed in telnes3.def). Each filename is followed by I or O (input/output), a short description of the file content, and a comment on when the file is used. case.innes (I). Defines the ELNES calculation. Always read. case.struct (I). Defines the crystal. Always read. case.vsp (I). Spherical component of the crystal potential. Read unless core and final state wavefunctions are read from file. case.vtotal (I). Total crystal potential (can be generated by lapw0). Read if EXTEND POTENTIAL is used. case.rotij (I). Rotation matrices that transform q-vectors between equivalent atoms. Read if INITIALIZATION tells the program to do so. case.dos (IO). l-resolved density of states. Read or written depending on INITIALIZATION settings.

198 180 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION case.xdos (IO). lm,l m -resolved density of states. Read or written depending on INITIALIZATION settings; only if the calculation is orientation resolved. case.qtl (I). contains partial charge components and Fermi energy. Read if DOS needs to be calculated (INITIALIZATION) or if Fermi energy is not specified using FERMI. case.inc (I). Specifies core states. Only read if core states are calculated. case.kgen (I). contains k-mesh to sample the Brillouin Zone. Read if DOS needs to be calculated. case.outputelnes (O). Main log file. Always written. Content depends on VERBOSITY. case.elnes (O). Total spectrum. Always written. case.sdlm (O). Partial (l,m) spectra. Written if verbosity > 0. case.ctr (O). (l,m,l m ) crossterms. Written if verbosity > 0 and calculation is orientation sensitive. case.corewavef (O). Contains core wavefunctions. Written if core wavefunctions were calculated and verbosity > 1. case.final (O). Contains APW radial basis functions for final states at selected energies. Written if verbosity > 1. case.ortho (O). Contains scalar products of initial and final states. Written if verbosity > 1. case.matrix (O). Proportionality between partial DOS and spectrum for each l-value. Written if verbosity > 0 and MODUS is energy. case.cdos (O). Selected (l,m,l m ) cross-dos terms. Written if calculation is orientation sensitive and verbosity > 1 or INITIALIZATION causes DOS to be written to file. case.sp2 (O). Integrated cross sections as a function of collection angle for all l-values. Written if calculation is orientation sensitive, MODUS is set to angle and verbosity > 1. case.angular (O). Differential cross section as a function of scattering angle for all l-values. Written if calculation is orientation sensitive, MODUS is set to angle and verbosity > 1. case.inb (O). Settings for the broadening program. Always written. case.eelstable (O). Placeholder. Not currently used. telnes3.def (I). List of files used by TELNES3. Always read. telnes3.error (O). Error file containing current error message; empty after successful calculation. Always written TETRA (density of states) This program calculates total and partial density of states (DOS) by means of the modified tetrahedron method (Blöchl et al 1994). Please note, the tetrahedron method will not work with just one k-point and tetra will automatically switch to a Gaussian broadening scheme (with default broadening of 0.01 Ry). The broadening schemes can also be selected by input (see below), but is not recommended for small unit cells. It uses the partial charges in case.qtl generated by the programs lapw2 (switch QTL) or qtl and generates the DOS in states/ry(cell (files case.dos1/2/3/...) and in states/ev(cell (with respect to the Fermi energy; files case.dos1/2/3ev). In spin-polarized calculations the DOS is given in states/ry/spin (or states/ev/spin). Alternatively and for the total DOS only, you can use the switch -enefile which does not require case.qtl, but uses case.energy and case.scf2 (in case of parallel lapw1 use cat case.energy 1 case.energy 2... case.energy ). Please note: The total DOS is equal to the sum over the atoms of the total-atomic DOS (inside spheres) and the interstitial-dos. (Thus in the total-atomic DOS the multiplicity of an atom is considered). On the other hand, in the partial (lm-like) DOS the multiplicity is not considered and one obtains the total-atomic DOS as a sum over all partial DOS times the multiplicity. The m-decomposed DOS (e.g. p z, p y, p x ) is given with respect to the local coordinate system for each atom as defined by the local rotation matrix (see Appendix A), unless you have used x qtl

199 8.22. TETRA 181 to generate the case.qtl and specified a specific coordinate system in case.inq (see Chapter 8.19). You can also direct tetra to sum-up some partial DOS components into a single DOS. This is for instance useful to sum over the different positions of one element. Using the switches -rxes E1 E2 it is possible to generate a weight-file, where each k-point is weighted according to its contribution to the DOS in the energy range E1-E2. This weight-file case.rxes can be used using the switch -rexs to calculate the DOS with these weights. This option might be useful to simulate the E-dependency of RXES spectra, or in general calculate a DOS of regions around selected k-points only. The density of states in files case.dos1/2/3/... or case.dos1/2/3/...ev can be plotted by dosplot2 lapw (see ). It is strongly recommended that you use Run Programs Tasks Density of States from w2web Execution The program tetra is executed by invoking the command: tetra tetra.def or x tetra [-up dn -enefile -so -hf -rxes -rxesw E1 E2] Dimensioning parameters The following parameters are listed in file param.inc: MG LXDOS max. number of DOS cases usually 1, except for cross-dos when using TELNES.2 = 3 (not needed anymore for TELNES3) Input The required input file case.int can optionally be created using the w2webinterface or the configure int lapw script (see 5.2.9). An example is given below: top of file: case.int TiO2 # Title # EMIN, DE, EMAX for DOS, GAUSS-Broad 7 N # NUMBER OF DOS-CASES, G/L/B broadening 0 1 tot # jatom, doscase, description 1 2 Ti-s 1 3 Ti-p 1 4 Ti-px 1 5 Ti-py 1 6 Ti-pz 2 1 O-tot SUM: 1 2 # NUMBER OF SUMMATIONS, max-nr-of summands 2 3 # this sums dos-cases 2+3 from the input above bottom of file Interpretive comments on this file are as follows: line 1: free format title

200 182 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION line 2: free format emin, delta, emax, broad emin, delta, emax broad specifies the energy mesh (in Ry) where the DOS is calculated. (emin should be set slightly below the lowest valence band; emax will be checked against the lowest energy of the highest band in case.qtl, and set to the minimum of these two values; delta is the energy increment. Gauss-broadening factor. Must be greater than delta to have any effect. line 3: free format ndos, Bmethod, broadening ndos Bmethod G L B broadening specifies the number of DOS cases to be calculated. It should be at least 1. The corresponding output is written in groups of 7 to respective case.dosx files optional input (can be omitted) to select instead of the tetrahedron method: Gaussian broadening Lorentzian broadening both, Gauss and Lorentzian broadening parameters in Ry, typically below/around 0.01 (optional, specify two numbers for B) line 4: (2i5,3x,a6) jatom, jcol, description jatom jcol description specifies for which atom the DOS is calculated. 0 means total DOS, jatom = nat + 1 means DOS in the interstitial, where nat is the number of inequivalent atoms. When spin-orbit is included, jatom = nat + 1 gives total spin-up/dn DOS in a spinpolarized SO calculation, but is meaningless in a non-spinpolarized SO case. specifies the column to be used in the respective QTL-file. 1 means total, 2... s, 3... p,... The further assignment depends on the value of ISPLIT set in case.struct (see sec. 4.3); the respective description can be found in the header of case.qtl. text used for further identification. >>>:line 4 is repeated ndos times line 5: optional line (free format) SUM, nsum, isummax SUM the keyword SUM directs tetra to add-up some partial DOS specified in the lines above and produce case.dossum and case.dossumev. nsum number of summations as specified below (max 7). isummax max number of summands in the lines below. line 6: optional line (free format) iline1 iline2... iline1,2,.. gives the DOS-cases which should be summed up (max isummax cases).

201 8.23. XSPEC 183 >>>:line 6 is repeated nsum times 8.23 XSPEC (calculation of X-ray Spectra) This program calculates near edge structure of x-ray absorption or emission spectra according to the formalism described by Neckel et al.75, Schwarz et al. 79 and 80. For a brief introduction see below. It uses the partial charges in case.qtl. This file must be generated separately using lapw2. Partial densities of states in case.dos1ev are generated using the tetra program. Spectra are calculated for the dipole allowed transitions, generating matrix elements, which are multiplied with a radial transition probability and the partial densities of states. Unbroadened spectra are found in the file case.txspec, broadened spectra in the file case.xspec. Other generated files are: case.m1 (matrix element for the selection rule L+1) and case.m2 (matrix element for the selection rule L-1) and case.corewfx (radial function of the core state). The calculation is done with several individual programs (initxspec, tetra, txspec, and lorentz). which are linked together with the c-shell script xspec. It is strongly recommended that you use Run Programs Tasks X-ray spectra from w2web Execution Execution of the shell script xspec The program xspec is executed by invoking the command: xspec xspec.def or x xspec [-up -dn] Sequential execution of the programs Besides calculating the X-ray spectra in one run using the xspec script, calculations can be done by hand, i.e. step by step, for the sake of flexibility. initxspec This program generates the appropriate input file case.int, according to the dipole selection rule, for the subsequent execution of the tetra program. The program initxspec is executed by invoking the command: initxspec xspec.def or x initxspec [-up -dn] tetra The appropriate densities of states for (L+1) and (L-1) states respectively are generated by execution of the tetra program. The program tetra is executed by invoking the command: tetra tetra.def or x tetra [-up -dn] txspec This program calculates energy dependent dipole matrix elements. Theoretical X-ray spectra are generated using the partial densities of states (in the case.dos1ev file) and multiplying them with the corresponding dipole matrix elements. The program txspec is executed by invoking the command: txspec xspec.def or x txspec [-up -dn] lorentz The calculated spectra must be convoluted to account for lifetime broadening and for a finite resolution of the spectrometer before they can be compared with experimental spectra. In the lorentz program a Lorentzian is used to achieve this broadening. The program lorentz is executed by invoking the command: lorentz xspec.def or x lorentz [-up -dn]

202 184 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION If you want orientation sensitive XSPEC (like p-parallel and p-normal spectra, you may change in case.int the column-number to eg. p x or p z and rerun the last tree steps of the script above mnually Dimensioning parameters The following dimensioning parameters are collected in the files param.inc of SRC txspec and SRC lorentz: IEMAX0 NRAD LMAX maximum number of energy steps in the spectrum (SRC lorentz) number of radial mesh points highest l+1 in basis function inside sphere (consistent with input in case.in1) Input Two examples are given below; one for emission spectra and one for absorption spectra: Input for Emission Spectra: top of file: case.inxs NbC: C K (Title) 2 (number of inequivalent atom) 1 (n core) 0 (l core) 0,0.5,0.5 (split, int1, int2) -20,0.1,3 (EMIN,DE,EMAX in ev) EMIS (type of spectrum, EMIS or ABS) 0.35 (S) 0.25 (gamma0) 0.3 (W) AUTO (generate band ranges AUTOmatically or MANually (E0 in ev) (E1 in ev) (E2 in ev) bottom of file Input for Absorption Spectra: top of file: case.inxs NbC: C K (Title) 2 (number of inequivalent atom) 1 (n core) 0 (l core) 0,0.5,0.5 (split, int1, int2) -2,0.1,30 (EMIN,DE,EMAX in ev) ABS (type of spectrum) 0.5 (S) 0.25 (gamma0) bottom of file Interpretive comments on these files are as follows. line 1: free format TITLE Title line 2: free format NATO Number of the selected atom (in case.struct file)

203 8.23. XSPEC 185 line 3: free format NC principle quantum number of the core state line 4: free format LC azimuthal quantum number of the core state The table below lists the most commonly used spectra: line 5 free format Spectrum n l K 1 0 L II,III 2 1 M V 3 2 Table 8.116: Quantum numbers of the core state involved in the x-ray spectra SPLIT, INT1, INT2 split in ev between e.g. L II and L III spectrum (compare with the respective core eigenvalues), INT1 and INT2 specifies the relative intensity between these spectra. Values of 0, 0.5, 0.5 give unshifted spectra. line 6: free format EMIN, DE, EMAX minimum energy, energy increment for spectrum, maximum energy; all energies are in ev and with respect to the Fermi level EMIN and EMAX are only used as limits if the energy range created by the lapw2 calculation (using the QTL switch) is greater than the selected range. line 7: Format A4 TYPE EMIS X-ray emission spectrum ABS X-ray absorption spectrum (default) line 8: free format S broadening parameter for the spectrometer broadening. For absorption spectra S includes both experimental and core broadening. Set S to zero for no broadening. line 9: free format GAMMA0 broadening parameter for the life-time broadening of the core states. Set GAMMA0 to zero to avoid lifetime broadening of the core states. line 10: free format W broadening parameter for the life-time broadening of valence states. Set W to zero to avoid lifetime broadening of the valence states. line 11: format A4

204 186 CHAPTER 8. ANALYSIS, PROPERTIES AND OPTIMIZATION BANDRA AUTO MAN band ranges are determined AUTOmatically (default) band ranges have to be entered MANually line 12: free format E0 Emission spectra: onset energy for broadening, E0, generated automatically if AUTO was set in line 10 Absorption spectra: not used line 13: free format E1 Emission spectra: onset energy for broadening, E1, generated automatically if AUTO was set in line 10 Absorption spectra: not used line 14: free format E2 Emission spectra: onset energy for broadening, E2, generated automatically if AUTO was set in line 10 Absorption spectra: not used

205 9 Utility Programs Contents 9.1 symmetso pairhess eigenhess patchsymm afminput clmcopy reformat hex2rhomb and rhomb in plane add columns clminter eosfit eosfit spacegroup join vectorfiles arrows xyz2struct cif2struct Tmaker struct2cif struct2poscar conv2prim fleur2wien StructGen of w2web supercell structeditor Visualization Unsupported software symmetso This program helps to setup spin-orbit calculations in magnetic systems. Since SO may break symmetry in certain spacegroups, it classifies your symmetry operations into operations A, which do not invert the magnetization (identity, inversion, rotations with the rotation axis parallel to magnetization), B, which invert it (mirror planes) and C, which change the magnetization in some 187

206 188 CHAPTER 9. UTILITY PROGRAMS other way. (Note: magnetization is a result of a circular current, or equivalently, an axial vector resulting from a vector product ẑ ˆx ŷ). symmetso will keep all A-type and throw away all C-type symmetry operations. Depending on the presence of inversion symmetry it will keep (inversion is present) or remove the B-type operations. Finally, symmetso uses the remaining symmetry operations to check/generate equivalent atomic positions (it can happen that some equivalent atoms become non-equivalent after inclusion of SO interaction). In essence, it reads your case.struct and case.inso (for the direction of magnetization) files and creates an ordered case.struct orb file with proper symmetry and equivalent atoms. It also generates a file case.ksym, which is a struct file with valid operations to generate a proper k-mesh using x kgen -so. In addition proper input files case.in1, case.in2, case.inc, case.vspup/dn, case.vnsup/dn, case.clmsum, case.clmup/dn are generated, so that you can continue with runsp -so without any further changes Execution The program symmetso is executed by invoking the command: symmetso symmetso.def or x symmetso [-c] Usually it is called from the script initso lapw and thus needs not to be invoked manually. 9.2 pairhess This program was contributed by: James Rondinelli, Bin Deng and Laurence Marks Dept. Materials Science and Engineering Northwestern University Evanston, USA Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. This program creates an approximate hessian matrix (in.minpair) for structure minimization using the PORT option. It uses a harmonic model with exponentially decaying bond strenght and in many cases reduces the number of geometry steps during min lapw significantly. It is described in detail in Rondinelli et al For its usage see the comments in sect Execution The program pairhess is executed by invoking the command: pairhess pairhess.def or x pairhess [-copy] The switch -copy copies.minpair to.minrestart and.min hess, which are needed in min lapw.

207 9.2. PAIRHESS Dimensioning parameters The following parameters are used in param.inc: NATMAX NEIGMAX max. number of atoms) max number of neighbours Input pairhess uses an optional input file case.inpair, which is needed only for an experienced user for better tailoring of certain default parameters. An example is given below: top of file: case.inpair (Rmax, Decay, ReScale) (Cutoff, Diag, mode) 0.2 (ZWEIGHT Interpretive comments on this file are as follows: line 1: free format RMAX Maximum distance (a.u.) for considering neighbors is good. DECAY Exponential decay applied to neighbors when calculating the pairwise bond strenghts is reasonable. RESCALE A scaling term to multiply the pairwise hessian by. This number is rather important; 0.25 appears to be best for a system with soft modes, 0.35 for a stiffer system. You can save substantial time by adjusting RESCALE so it is approximately correct using a.min hess from a previous run (adjust until numbers for similar multiplicities are similar), or by adjusting the frequencies (see also eigenhess). line 2: free format CUTOFF When the weighting (via an exponential decay) becomes smaller than this number the pairwise bonds are ignored. DIAG The value to multiply a unitary matrix by, this is added to the hessian estimate MODE 0: Spring model; [1: harmonic model; not so good] line 3: free format ZWEIGHT Atomic number weight for bonds of form exp(-z*zweight). Values of are reasonable. The default is 0.1; a negative number (e.g. -1) turns this off.

208 190 CHAPTER 9. UTILITY PROGRAMS 9.3 eigenhess This program was contributed by: Laurence Marks Dept. Materials Science and Engineering Northwestern University Evanston, USA Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. This program analyses / manipulates.min hess, which was created by a structural minimization using min lapw and the PORT option. In particular, such an analysis can yield approximate vibrational frequencies and corresponding eigenmodes, which eventually can give a hint about a dynamically unstable structure (imaginary frequencies). Some more description is given in $WIENROOT/SRC pairhess/readme. The program eigenhess is executed by invoking the command: x eigenhess 9.4 patchsymm This program was contributed by: James Rondinelli, Bin Deng and Laurence Marks Dept. Materials Science and Engineering Northwestern University Evanston, USA Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. This program performs a symmetry check on the positions and produces a new struct file case.struct new. It is useful in case something went wrong during min lapw (rounding errors of positions) or the cif/amc file did not have enough digits (eg. 1/3 was prepresented by only). The file case.outputpatch gives information on how parameters changed Execution The program patchsymm is executed by invoking the command: patchsymm patchsymm.def or x patchsymm

209 9.6. CLMCOPY afminput This program creates the inputfile case.inclmcopy st for the program clmcopy, which copies spin-up densities of atom i to spin-down densities of the related antiferromagnetic atom j and vice versa in an anti-ferromagnetic system. It uses a symmetry operation to find out how and which atomic densities must be interchanged and how the Fourier coefficients of the density transform. It is based on the ideas of Manuel Perez-Mato (Bilbao, Spain). See $WIENROOT/SRC afminput/afminput test for several examples. The best way is to supply a file case.struct supergroup, which is the struct file of the nonmagnetic supergroup. If the two spacegroups are TRANSLATIONENGLEICH, it will find out automatically the proper symmetry operation. Please note, this automatic way works only when the coordinate system remains identical. In some cases sgroup may interchange eg. the y and z axis. In such cases reverse this change, both, for the lattice parameters as well as for all positions, set NSYM=0 and run init lapw again (ignoring any suggestion of sgroup). If the two spacegroups are KLASSENGLEICH (i.e. have the same number of symmetry operations), you will be asked to supply a translation which transforms the AF atoms into each other. A typical example would be bcc Cr: the bcc supergroup and the AF subgroup (simple cubic) have both 48 symmetry operations and the proper translation is (0.5,0.5,0.5). Finally, if you don t give case.struct supergroup, you have to supply a symmetry operation (rotation + non-primitive translation) as input. For bcc Cr or the famous NiO-AFII structure this would be simply Please see the comments in sect on how to proceed in detail for AFM calculations and find further examples in SRC afminput Execution The program afminput is executed by invoking the command: afminput afminput.def or x afminput Dimensioning parameters The following parameters are used: NCOM LMAX number of LM components in the density (in param.inc) max l for LM expansion of the density (in param.inc). 9.6 clmcopy This program generates the spin-dn density (case.clmdn) from a given spin-up density (case.clmup) according to rules and symmetry operations in case.inclmcopy (generated earlier by afminput) for an AFM calculation. Please see the comments in sect on how to proceed in detail for AFM calculations.

210 192 CHAPTER 9. UTILITY PROGRAMS Execution The program clmcopy is executed by invoking the command: clmcopy clmcopy.def or x clmcopy Dimensioning parameters The following parameters are used in param.inc: NCOM NRAD NSYM number of LM components in the density number of radial mesh points number of symmetryoperations Input An example is given below: top of file: case.inclmcopy NUMBER of ATOMS to CHANGE 1 2 INTERCHANGE these ATOMS SYMMETRY OPERATION NUMBER of LM to CHANGE SIGN 3 4 INTERCHANGE these ATOMS SYMMETRY OPERATION NUMBER of LM to CHANGE SIGN Interpretive comments on this file are as follows: line 1: free format NATOM Number of atoms for which rules for copying the density will be defined line 2: free format N1, N2 Interchange spin-up and dn densities of atoms N1 and N2 line 3-5: free format SYM Symmetry operation for atom N1 to rotate into N2 (without translational part)

211 9.7. REFORMAT 193 line 6: free format NLM Number of LM values, for which you have to change the sign when swapping up and dn-densities line 7ff: free format L1,M1,L2,M2,Fac NLM pairs of L1,M1 (spin-up), which change into L2,M2 (spin-dn) and the respecting CLMs are multiplied by Fac Lines 2-7ff have to be repeated NATOM times. line 8-10: free format SYM0 Symmetry operation (one of the operations of the NM-supergroup missing in the AFM-subgroup (transfers spin-up into spin-dn atom) 9.7 reformat To produce a surface plot of the electron density using rhoplot lapw (which is an interface to gnuplot), data from the file case.rho created by lapw5 must be converted using reformat The sources of the program reformat.c are supplied in SRC reformat. 9.8 hex2rhomb and rhomb in5 hex2rhomb interactively converts the positions of an atom from hexagonal to rhombohedral coordinates (needed in case.struct). rhomb in5 interactively helps to generate input case.in5 for density plots with lapw5 for rhombohedral systems. It defines a plane as needed in the input file when you specify 3 atoms of that plane. The sources of these programs are supplied in SRC trig. 9.9 plane plane helps to generate case.in5 for density plots with lapw5 (for orthogonal and hex lattices only). The plane will be specified by 3 atoms and you need an auxiliary file plane.input, which contains: a,b,c x0,y0,z0 x1,y1,z1 x2,y2,z2 xl,yl P # lattice parameters # position of atom (fractional coordinates), which will be centered in the plot # position of atom, which will be below the centered atom # position of atom, which will show to the left # lenght (in bohr) of plot in x and y direction. # defines lattice, either P (cartesian coordinates) or H (hexagonal) supported The source of this program is supplied in SRC trig.

212 194 CHAPTER 9. UTILITY PROGRAMS 9.10 add columns add columns reads a sequence of pairs of 2 numbers (form stdin), adds them together and prints the sum to stdout. If you have two columns of numbers in 2 files (eg. in colup and coldn) you can add them using: paste colup coldn add columns > col The source of this program is supplied in SRC trig clminter clminter interpolates the density in case.clmsum/up/dn to a new radial mesh as defined in case.struct new. This utility is useful when you run a structural minimization (min lapw), some atoms start to overlap and you have to reduce RMT (the size of the atomic spheres) of certain atoms. In such a case: save the calculations generate case.struct new with modified RMTs x clminter in spinpolarized case repeat this line with -up and -dn switches cp case.struct new case.struct cp case.clmsum new case.clmsum eventually copy also case.clmup/dn files) run lapw; (it will probably take some iterations until you reach scf again, but it should be much faster than starting with init lapw) Note: Please be aware the the total energy will change with modified RMT (by some constant) and you must not compare energies comming from different RMTs (but most likely you can determine the constant shift by repeating (at least) ONE calculation with identical structure but different RMTs). The source of this program is supplied in SRC trig eosfit Small program to calculate the Equation of States (EOS; Equilibrium volume V 0, Bulk modulus B 0 and it s derivative B 0. The Murnaghan (1944), the Birch-Murnaghan and the EOS2 equation of states are supported. It relies on the file case.vol (containing lines with volume, E-tot, usually created from w2web using Volume optimization ), or alternatively is called from eplot lapw using case.analysis (see and 5.3.1). The sources are supplied in SRC eosfit eosfit6 Nonlinear least squares fit (using PORT routines) for a parabolic fit of the energy vs. 2-4 dim. lattice parameters. It requires case.ene and case.latparam, usually generated by parabolfit lapw. It can optionally produce case.enefit, which contains energies on a

213 9.14. SPACEGROUP 195 specified grid for plotting purposes (in 2D same format as case.rho, which can be used in contourplot programs). (See 5.3.1). The sources are supplied in SRC eosfit spacegroup This program was contributed by: Vaclav Petricek Institute of Physics Academy of Sciences of the Czech Republic Na Slovance Praha (Prague) 8 Czech Republic Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. Interactive program to generate equivalent positions for a given spacegroup and lattice. The program is also used internally from w2web to generate positions when selecting spacegroups in the StructGen join vectorfiles This program was contributed by: Phillipp Wissgott Institute of Solid State Physics TU Vienna Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. Interactive program to combine parallel vector and energy files (case.vector xx and case.energy xx) into single files (case.vector and case.energy). Executed by: x join vectorfiles [-up/-dn/-so/-soup/-sodn] [-c] case number of parallel files to join 9.16 arrows This program was contributed by:

214 196 CHAPTER 9. UTILITY PROGRAMS Evgeniya Kabliman Institute for MaterialsChemistry TU Vienna Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. Small program which together with Xcrysden allows to display the forces acting on all atoms or the differences between two structures using arrows which indicate the movement of the atoms. The recommended sequence to visualize forces is: Prepare (copy) a struct and scf file with the initial structure using the names case initial.struct and case initial.scf. View case initial.struct in Xcrysden and File/Save as xsf-structure with the name case initial.xsf. x arrows View the resulting case forces.xsf using: xcrysden --xsf case forces.xsf. Switch on Display/Forces and adjust the length of the arrows in Modify/Force-settings. while differences between the inital and relaxed structure can be viewed by: Prepare (copy) two struct files with the initial and the relaxed structure using the names: case initial.struct and case final.struct. View case initial.struct in Xcrysden and File/Save as xsf-structure with the name case initial.xsf. x -delta arrows View the resulting case delta.xsf using: xcrysden --xsf case delta.xsf. Switch on Display/Forces and adjust the length of the arrows in Modify/Force-settings xyz2struct xyz2struct reads atomlabel,x,y,z -data from case.xyz and writes them into xyz2struct.struct. You may have to edit the xyz-file and insert a few lines at the top: ANG(default)/BOHR; F/C (fractional or cart. coordinates) and L (lattice information, see example) a,b,c lattice parameters, or when L was specified a scaling constant and the bravais matrix. Since xyz data contain no symmetry information, all atoms with the same label will be treated as equivalent. The nuclear charges ZZ will not be given and you have to insert them manually or use w2web-structgen. It is executed using: xyz2struct < case.xyz (I recommend this program only for cases with many non-equivalent atoms and (almost) no symmetry. If you have spacegroup-information it is probably easier to use StructGen and copy/paste of the positions). A proper case.xyz file looks like:

215 9.18. CIF2STRUCT 197 ang B C or BOHR F L B C cif2struct cif2struct reads structural data in cif-format from case.cif and writes them into case.struct. It is executed using: cif2struct case.cif or cif2struct case.txt or x cif2struct [-txt] The required cif files can be for example be obtained from Cystallographic databases (e.g. the Inorganic Crystal Structure DataBase ICSD) or from other programs (when transfered from MS-Windows, make sure to habe it in Unix-mode, not in Dos-mode ; eventually use dos2unix ). Alternatively, cif2struct can work with case.txt, which contains the following data: a # a..ang, b..bohr # shift of origin # a,b,c,angles R-3c # spacegroup-symbol (see \STRUCTGEN{}) Al # atom-name # atomic position O # # Tmaker Tmaker creates a struct-file init.struct from a file datastruct, which can be created by the script makestruct lapw. It is executed using: Tmaker It was contributed by Morteza Jamal(m 9.20 struct2cif struct2cif creates a cif-file case.cif from case.struct. It is executed using: x struct2cif or struct2cif struct2cif.def It was contributed by F. Boucher and L.D.Marks In order to work properly, the case.struct file should have a spacegroup label included. There is also a similar program struct2xyz available.

216 198 CHAPTER 9. UTILITY PROGRAMS 9.21 struct2poscar struct2poscar creates the files case.poscar and case.xyz from case.struct. case.poscar and case.xyz are files which are used by the package dftd3 when periodic boundary conditions are switched on or off, respectively. It is executed using: x struct2poscar or struct2poscar struct2poscar.def 9.22 conv2prim conv2prim creates the file case prim.struct which corresponds to the primitive cell of the conventional unit cell specified by case.struct. It is executed using: x conv2prim or conv2prim conv2prim.def 9.23 fleur2wien fleur2wien converts the FLEUR-file which contains the exchange-correlation potential (case.potential) into the WIEN2k-format (case.r2v(dn)). The FLEUR-file case.lattice harmonics, which contains the linear combinations of spherical harmonics, is also necessary. If the FLEUR and WIEN2k Bravais matrices are not the same, then the FLEUR direct Bravais matrix has to be specified at the beginning of case.lattice harmonics below the keyword bravais (a, b, c lattice parameters specified at the 1st, 2nd, 3rd lines, respectively). It is executed using: x fleur2wien or fleur2wien fleur2wien.def 9.24 StructGen of w2web The new StructGen helps to generate the master input file case.struct. It has the following additional features: automatic conversion from/to Å and Bohr Use spacegroup information (in conjunction with the spacegroup program (see 9.14 to generate equivalent positions) built in calculator to carry out simple arithmetic operations to specify the position pameters (of the equivalent atoms). Each position of equivalent atoms can be entered as a number, a fraction (e.g. 1/3) or a simple expression (e.g /3). The first position defines the variables x, y and z, which can be using in expression defining the other positions (e.g. y, x, z + 1/2) supercell This program helps to generate supercells from a regular WIEN2k-struct file. It asks interactively for the name of the original struct file and the number of cells in x, y, and z direction. (Only integers are allowed, thus no rotations by 45 o like sqrt(2) x sqrt(2) cells are supported yet).

217 9.26. STRUCTEDITOR 199 If symmetry permits, one can change the target lattice to P, B or F centered lattices, which allows to increase the number of atoms in these supercells by a factor of 2, 4, 8,... Rhombohedral (R) lattices are converted automatically into H (hexagonal) lattices, which are 3 times larger than the original cell. If the target lattice is P, one can add some vacuum in each direction for surface slabs (or chains or isolated molecules) and also add a top -layer (repeat the atoms with z=0 at z=1). You can define an optional shift in x,y,z direction for all the atoms in the cell. (This might be useful if you want to arrange the atoms in a certain way, eg. you may want to create a surface slab such that it is centered around z=0.5 (and not z=0), so that plotting programs (xcrysden) produce nicer pictures of the structure. For the experienced user a much more flexible (but also more complicated) tool is available, namely the structeditor package (see Sect.9.26). Please note: You cannot make calculations with these supercells (except for surfaces) unless you modify the created supercell-struct file. You must break the symmetry by introducing some distortions (e.g. for a frozen phonon) or replace one atom by an impurity/vacancy, Execution The program supercell is executed by invoking the command: supercell or x supercell 9.26 structeditor This program was contributed by: Robert Laskowski Please make comments or report problems with this program to the WIEN-mailinglist. If necessary, we will communicate the problem to the authors. This package helps to manipulate structures. Usually one would start from an appropriate (simple) case.struct file, and this tool allows to add or manipulate atoms (with or without symmetry considerations), or generate arbitrary supercells or surfaces. It is commandline driven and targeted for the more experienced user, who knows what he wants to do and is just looking for a convenient tool. It consists of a couple of octave (matlab) routines and some fortran code, thus it requires octave (the free matlab version) and for visualization the xcrysden program. A more extended documentation and some examples can be found in $WIENROOT/SRC structeditor/doc, but the most important command helpstruct lists all available functions: a2adist * calculates distance between atoms mina2adist * calculates minimum distance between atoms addatom * adds an atom to the structure addeqatom * adds an atom and all equivalent

218 200 CHAPTER 9. UTILITY PROGRAMS copyatom getaname getar0 getazz loadstruct makeconventional makeprimitive makesupercell makesurface mergestruct movealla replaceatom replaceeqatoms rescale_c rescale_c_2 rescale_c_3 rmatom rmeqatoms rotateall rotateatomlist rotatethreedim savestruct shiftatomlist showequivalent showstruct smultatom sshift * creates a copy of an atom * converts atomic number into atomic symbol * calculates r0 from atomic number * converts atomic name into atomic number * reads Wien2k structfile * convestrs structure into the conventional form * converts structure to the primitive form * creates supercell * creates surface * merges two structures * moves all atoms with vector vec * replaces an atom with other atom * replaces an atom and all equivalent with other atoms * rescales c for surface cell (vacume in the midle) * rescales c for surface cell (vacume above) * rescales c for surface cell (vacume audside) * removes an atom * removes an atom and all equivalent * rotates all atoms around z with a given angle * rotates specified atoms around z with a given angle * rotates specified atom around vector with given angle * saves crystal structure * shifts specified atoms by a vector * outputs list of equivalent atoms * displays structure (using DX) * creates symmetry equivalent positions * symmetric shifts of equivalent atoms You can get then specific help on a particular function using eg.: help makesurface. PS: It is also fairly trivial to construct new functions starting from already existing ones or by combining them in a convenient way Execution The structeditor is invoked within the octave environment and a typical sequence of commands could be: octave s=loadstruct( GaN.struct ) # make an orthorhombic supercell and visualize it a=[1 0 0; 1 1 0; 0 0 2] sout=makesupercell (s,a); showstruct(sout); # save it as test.struct savestruct (sout, test.struct ); # get help on all commands helpstruct # get help on the command makesupercell help makesupercell

219 9.27. VISUALIZATION Visualization BALSAC balsac (Build and Analyze Lattices, Surfaces and Clusters) was written by Klaus Hermann (Fritz-Haber Institut, Berlin). It provides high quality postscript files. In SRC balsac-utils we provide the following interface programs to convert from WIEN2k to balsac: str2lat to convert case.struct to case.lat (the BALSAC lat file). str2plt to convert case.struct to case.plt (the BALSAC plt file for one unit cell). outnn2plt to convert case.outputnn to case.plt (the BALSAC plt file for one unit cell). You have to select one atom (central atom) and than all nn-atoms are converted into the plt file. In addition converters to the xyz-format (str2xyz, outnn2xyz) for other plotting programs are also available. For an example see figure 3.1 For scientific questions concerning BALSAC please contact Klaus Hermann at Balsac is available from: Garching Innovation GmbH, Mrs. M. Pasecky Hofgartenstr. 8, D Munich, Germany Tel.: , Fax.: web: XCrysDen XCrysDen (Kokalj 1999) is a render and analysis package. It has the following features (see also render and analyze (distances, angles) the crystal structure generate k-mesh for bandstructure plots generate input and render 2D charge densities generate input and render 3D charge densities generate input and render Fermi surfaces render changes between two structures (original and relaxed) with the help of the arrows program (see 9.16) XCrysDen is available from: Tone Kokalj Jozef Stefan Institute, Dept. of Physical and Organic Chemistry Jamova 39, SI-1000 Ljubljana, Slovenia Tel.: , Fax:

220 202 CHAPTER 9. UTILITY PROGRAMS Figure 9.1: 3D electron density in TiC generated with XCrysDen 9.28 Unsupported software On our website you can find a link to Unsupported software goodies, where references to various software packages are given. Most of those packages are contributions from WIEN2k-users and you may check this site from time to time if you find some useful tools for you. In case you develop some goodies yourself and want to share this development with the WIEN2k community, please send an to and we will add it to this page.

221 10 How to run WIEN2k for selected samples Three test cases are provided in the WIEN2k package. They contain the two starting files case.struct and case.inst and all the output so that you can compare your results with them. The test cases are the following (where the names correspond to what was called CASE in the rest of this User s Guide) TiC Fccni TiO2 We recommend to run these test cases (in a different directory) and compare the output to the provided one. All test cases are setup such that the CPU-time remains small (seconds). For real production runs the value of RKMAX in case.in1 must be increased and a better (denser) k-mesh should be used. In addition we provide a subdirectory example struct files were various more complicated struct files can be found TiC The TiC example is described in detail in chapter 3 (Quickstart) Fcc Nickel (spin polarized) Ferromagnetic Nickel is a test case for a spin-polarized calculation. Ni has the atomic configuration 1s 2, 2s 2, 2p 6, 3s 2, 3p 6, 3d 8, 4s 2 or [Ar] 3d 8, 4s 2. We treat the 1s, 2s, 2p and 3s as core states, and 3p (as local orbital), 3d, 4s and 4p are handled as valence states. In a spin-polarized calculation the file structure and the sequence of programs is different from the non-spin-polarized case (see 4.5.2). Create a new session and its corresponding directory. Generate the structure with the following data (we can use a large sphere as you will see from the output of nn): 203

222 204 CHAPTER 10. EXAMPLES Title fcc Ni Lattice F a 6.7 bohr b 6.7 bohr c 6.7 bohr α, β, γ 90 Atom Ni, enter position (0,0,0) and RMT = 2.3 Initialize the calculation using the default RKmax and use 3000 k-points (a ferromagnetic metal needs many k-points to yield reasonably converged magnetic moments). Allow for spin-polarization. Start the scf cycle (runsp lapw) with -cc (in particular for magnetic systems charge convergence is often the best choice). At the bottom of the converged scf-file (Fccni.scf) you find the magnetic moments in the interstital region, inside the sphere and the total moment per cell (only the latter is an observable, the others depend on the sphere size). :MMINT: MAGNETIC MOMENT IN INTERSTITIAL = :MMI001: MAGNETIC MOMENT IN SPHERE 1 = :MMTOT: TOTAL MAGNETIC MOMENT IN CELL = Rutile (T io 2 ) This example shows you how to optimize internal parameters and do a k-point parallel calculation. Create a new session and its corresponding directory. Generate the structure with the following data (we use a smaller O sphere because Ti-d states are harder to converge then O-p): Title TiO2 Spacegroup P 4 2/mnm (136) a bohr b bohr c bohr α, β, γ 90 Atom Ti, enter position (0,0,0) and RMT = 2.0 Atom O, enter position (0.3,0.3,0) and RMT = 1.6 StructGenshould automatically add the equivalent positions. Initialize the calculation using RKmax=6.5 in tio2.in1 st and use 100 k-points and a shift in kgen. If you have more cpus available (a parallel machine or simply a couple of PCs with a common NFS filesystem, for details see 5.5), you can use Execution Run scf, activate the parallel button and start scf in w2web. This will create and open a.machines file and you should insert lines with the proper names of your PCs (possibly use 9 (or 3) processors since we have 9 k-points, ). Save this file and click on Execution Run scf, activate -fc 1.0 for force-convergence and start scf to submit the scf-cycle. Alternatively at the command-line you can use the UNIX command cp $WIENROOT/SRC_templates/.machines. and edit this file. You would start the scf-cycle (in background) simply by typing run_lapw -p -fc 1.0 &

223 10.4. SUPERCELL CALC 205 During the scf-cycle monitor tio2.dayfile and check convergence (:ENE, :DIS, :FGL002), either using Utils/Analysis in w2web, or grep :ENE tio2.scf. You should see some convergence of :FGL002 and then a big jump in the final cycle, when the valence-force corrections are added. Only the last force (including this correction) is valid. Since this force is quite large, you can now optimize the position of the O-atom: Start the structure minimization in w2web using Execution mini.positions. This will generate TiO2.inM, and you can try option PORT with tolf=1.0 (instead of 2.0), otherwise stay with the default parameters. Repeat Execution mini.positions and start the minimization. Alternatively you can use min_lapw -p which is identical to: min_lapw -j run_lapw -I -fc 1 -p This will create TiO2.inM automatically, call the program min, which generates a new struct file using the calculated forces, and continues with the next scf cycle. It will continue until the forces are below 1 mry/bohr (TiO2.inM) and the final results are not saved automatically but can be found in the current calculation. You should watch the minimization (:ENE, :FGL002, :POS002) using the file TiO2.scf mini, which contains the final iteration of each geometry step (see also Sec.5.3.2). If the forces in this file oscillate from plus to minus and seem to diverge, or if they change very little, you can edit TiO2.inM (change the method, reduce or increase the stepsize), and remove TiO2.tmpM (contains the history of the minimization and is used to calculate the velocities of the moving atoms). (This should not be neceaasry for the rutile example, but may occur in more complex minimizations. See comments in Sec ). The final structural parameter of the O-atom should be close to x=0.304, which compares well with the experimental x= Supercell calculations on TiC This example shows you how to create a supercell of TiC, which could be used to simulate a TiC-surface or vacancies, impurities or core-holes for X-ray absorption / ELNES spectroscopy. I ll describe the procedure using Unix and WIEN2k commands in an xterm, but of course you can do the same in w2web. Create a new directory, copy the original TiC struct file into it and run supercell program: mkdir super cd super cp../tic/tic.struct. x supercell Specify TiC.struct, a 2x2x2 supercell, F lattice (this will create a cell with 16 atoms, you can also create 32 or 64 atom cells using B or P lattice type. Note: surfaces require a P supercell). cp TiC_super.struct super.struct and edit this file to make some changes. You could eg.

224 206 CHAPTER 10. EXAMPLES delete an atom (to simulate a vacancy) replace an atom by another element (impurity) label an atom (put a 1 in the 3rd column next to the element name) to make this atom unique (needed eg. for core-holes) displace an atom (for phase transitions or phonons) Note: it is important to make at least one of these chages. Otherwise the initialization will restore the original unit cell (or the calculations will fail later on because symmetry is most likely not correct) Run init lapw. You will see that nn complains and finds a new set of equivalent atoms (originally all atoms were non-equivalent, but nn finds that some atoms have identical neighbors, thus should be in an equivalent set). Accept the automatically generated struct file and continue. Remember, supercells normally require less k-points than the original small cell. After the complete initialization you may in principle restore the original struct file (eg. without a displacement) in case you want to repeat the undistorted structure in supercell geometry. For a core-hole calculation you would now edit super.inc and remove one core electron from the desired atom and state (1s or 2p,...). In addition you should add the missing electron either in super.inm (background charge) or super.in2 (add it to the valence electrons). In the latter case, you should remove this extra electron AFTER scf and BEFORE calculation of the spectra. Once this has been done, you could start a scf-cycle (for impurities, vacancies,.. you should most likely also optimize the internal positions) Further examples Further examples can be found on our web-site: or

225 Part III Installation of the WIEN2k package and Dimensioning of programs 207

226

227 11 Installation and Dimensioning Contents 11.1 Requirements Installation of WIEN2k w2web Environment Variables Requirements WIEN2k is written in FORTRAN 90 and requires a UNIX operating system since the programs are linked together via C-shell scripts. It has been implemented successfully on the following computer systems: Intel and AMD based PCs running under Linux, IBM RS6000, HP, SGI, and Mac. Hardware requirements will change from case to case (small cases with 10 atoms per unit cell can be run on almost any PC under Linux), but we recommend a more powerful quad-core Intel-core2 PC with at least 4 GB (better 8-16GB GB) memory and plenty of disk space (a TB). For coarse grain parallization on the k-point level, a cluster of PCs with a Gb Ethernet is sufficient. Faster communication (Infiniband) is recommended for the fine grain (single k-point) parallel version. For Intel (AMD) based systems we recommend the Intel ifort compiler and the Intel mkl library (which includes blas, lapack and Scalapack) (see If you have installed ifort yourself on your local PC, don t forget to configure your environment properly. Add some thing like: source /opt/intel/11.0/074/bin/ifortvars.csh intel64 source /opt/intel/11.0/074/mkl/tools/environment/mklvarsem64t.csh to your.cshrc file (or similar statements for.bashrc). In order to use all options and features (such as the new graphical user interface w2web or some of its plotting tools) the following public domain program packages in addition to a F90 compiler must be installed: perl 5 or higher (for w2web only) emacs or another editor of your choice ghostscript (with jpg support) gnuplot (with png support) www-browser pdf-reader, acroread 209

228 210 CHAPTER 11. INSTALLATION AND DIMENSIONING Tcl/Tk-Toolkit (for Xcrysden only) MPI+SCALAPACK (for fine grain parallelization only) FFTW v.2 or 3 (mpi-version for fine grain parallelization only) Usually these packages should be available on modern systems. If one of these packages is not available it can either be installed from public domain sources (ask your computing center, use the WWW to search for the nearest location of these packages) or the corresponding configuration may be changed (e.g. using vi instead of emacs). Brief installation instructions for mpich and fftw are given below. None of the principal components of WIEN2k requires these packages, only w2web needs them Installation tips for mpich and fftw (either version or 3.3) This is only a brief guidance, you may need some Linux experience for this. Download the mpich1.2.7p1 and fftw /or fftw-3.3 sources from and (Please note, the fftw-3.x versions are incompatible with fftw-2.x, but both interfaces are available in WIEN2k using the -DFFTW2 or -DFFTW3 compiler option (in FOPT/FPOT during siteconfig lapw) unzip and untar the downloaded file Change into the expanded directories and configure the compilation. Define your fortran compiler (setenv FC ifort, or export FC=ifort) and use./configure prefix=/pathname to configure compilation. /pathname is the directory where the libraries should be installed (could be /opt/local or /usr/local or similar, you will have to specify this path again in the LDFLAGS). For fftw configuration add the enable-mpi switch. make make install (if you specified a system-directory like /usr/local you must have proper permissions for this step, eg. become root user) add the mpi-directory to your path (set path = ( /opt/mpich/mpich-1.2.7p1/bin $path )) Optionally, one can also use in the sequential (non-mpi) version of lapw0 and lapw2 the fftw routines. However, there is some speedup only when you use the MKL-fft routines, not the self-compiled fftw-binaries. The mkl-interface to fftw is not active by default, but you may have to compile it yourself. To do so (syntax for ifort12): cd $MKLROOT/interfaces/fftw2xf make libintel64 (or make libia32) in case you do not have icc installed, but use GNU-C (gcc) you must: edit makefile, and remove -D GNU from the line CC=gcc -D GNU (to remove additional from the object names) make libintel64 compiler=gnu add -DFFTW2 to FOPT in the Makefile of lapw0 and lapw2 add -lfftw2xf or -lfftw2xf gnu to R LIBS in the Makefile of lapw0 and lapw2 a similar procedure is available for fftw3 (just exchange above 2 by 3 in all statements) This may speedup the fft-parts of these programs a bit.

229 11.2. INSTALLATION OF WIEN2K Installation of WIEN2k Expanding the WIEN2k distribution The WIEN2k package comes as a single tar file (or you can download about 50 individual tar files separately), which should be placed in a subdirectory which will be your $WIENROOT directory (e.g../wien2k). In addition you can download three examples, namely TiC.tar.gz, TiO2.tar.gz and Fccni.tar.gz. Uncompress and expand all files using: tar -xvf wien2k 12.tar (skip this if you downloaded files separately) gunzip *.gz chmod +x./expand lapw./expand lapw You should have gotten the following directories:./src SRC_2Doptimize SRC_afminput SRC_aim SRC_arrows SRC_balsac-utils SRC_broadening SRC_cif2struct SRC_clmaddsub SRC_clmcopy SRC_dipan SRC_dstart SRC_elast SRC_eosfit SRC_eosfit6 SRC_filtvec SRC_fsgen SRC_hf SRC_initxspec SRC_irrep SRC_joint SRC_kgen SRC_kram SRC_lapw0 SRC_lapw1 SRC_lapw2 SRC_lapw3 SRC_lapw5 SRC_lapw7 SRC_lapwdm SRC_lapwso SRC_lcore SRC_lib SRC_lorentz SRC_lstart SRC_mini SRC_mixer SRC_nn SRC_optic SRC_optimize SRC_orb SRC_pairhess SRC_phonon SRC_qtl SRC_reformat SRC_sgroup SRC_spacegroup SRC_spaghetti SRC_structeditor SRC_sumhfpara SRC_sumpara SRC_supercell SRC_symmetry

230 212 CHAPTER 11. INSTALLATION AND DIMENSIONING SRC_symmetso SRC_telnes3 SRC_templates SRC_tetra SRC_trig SRC_txspec SRC_usersguide_html SRC_vecpratt SRC_w2web example_struct_files TiC TiO2 fccni Thus, each program has its source code (split into several files) in its own subdirectory. All programs are written in FORTRAN90 (except SRC sgroup and SRC reformat, which are in C). /SRC contains the users guide (in form of a postscript file usersguide.ps and as pdf-file usersguide.pdf), all c-shell scripts and some auxiliary files. /SRC usersguide html contains the html version of the UG. /Fccni, /TiC and /TiO2 contain three example inputs and the respective outputs. /example struct files contains a collection of various struct files, which could be of use especially for the less experienced user. /SRC templates contains various input templates. In addition to the expansion of the tar-files./expand lapw copies also all csh-shell scripts from /SRC to the current directory and creates links for some abbreviated commands Site configuration for WIEN2k At the end of expand lapw you will be prompted to start the script./siteconfig lapw When you start this script for the first time (file INSTALLDATE not present), you will be guided through the setup process. Later on you can use siteconfig lapw to redimension parameters, update individual packages and recompile the respective programs. During the first run, you will be asked to specify: your system; at this point system specific files (e.g. cputim.f will be installed. If your system is not listed, use the system generic, which should compile on any machine. your FORTRAN90 and C compilers; your compiler and linker options as well as the place for LAPACK and BLAS libraries. Depending on the system you selected, we have included some recommended compiler and linker options, which are known to work on our systems (use generic when you have problems here; see also sec ). On some systems it is required to specify LAPACK and BLAS libraries twice (i.e. R LIBS:-llapack lapw -lblas lapw -llapack lapw -lblas lapw). This generates Makefiles from the corresponding Makefile.orig in all subdirectories. configuration of parallel execution will ask whether your system is shared memory, so that default parameters can be set accordingly ( $WIENROOT/parallel options is the file where this information is stored). to configure parallel execution for distributed systems, specify the command to open a remote shell, which on most systems is rsh or ssh. You will then be asked wether you want to run fine-grained parallel. This is only possible if FFTW, MPI and SCALAPACK (included in newer mkl-versions) are installed on your system and requires a fast network (100Mb/s is not enough) or a shared memory machine. It pays off only for bigger cases (matrixsize > 5000).

231 11.2. INSTALLATION OF WIEN2K 213 You should define NMATMAX, i.e. the maximum matrixsize (number of basisfunctions). This value should be adjusted according to the memory of your hardware. Rough estimates are: NMATMAX= 5000 ==> 256MB (real, i.e. with inversion symmetry) NMATMAX=10000 ==> 1GB (real) (==> cells with about atoms/unitcell) If you choose it too large, lapw1 will start to page leading to inacceptable performance or a crash. NMATMAX will be automatically recuced (by 2) for complex (without inversion) cases and increased by NP E for mpi-parallel cases. Now you are prompted to compile all programs (this will be done using make) and the executables are copied to the $WIENROOT directory. Compilation might take quite some time. During compilation watch for error messages on the screen. If there are errors, you may need to change into the corresponding SRC * directory and examine file compile.msg for details. Common errors are wrong specification of compiler, linking or library options. In such cases, adopt the Makefile in this directory and recompile using make. Once you have proper options, correct them globally in siteconfig lapw and recompile. Later on you can use siteconfig lapw to change parameters, options or to update a package User configuration Each WIEN2k user should run the script userconfig lapw. This will setup a proper environment. The script userconfig lapw will do the following for you: set a path to WIEN2k programs set the stacksize to unlimited add aliases add environment variables ($WIENROOT, $SCRATCH) to your /.cshrc or /.bashrc file. Eventually you should also edit these files and set the $LD LIBRARY PATH variable (path where compiler-libs or blas-libraries are located). Note: This will work only when the csh, tcsh or bash-shell is your login shell. Depending on your settings you may have to add similar lines also in your.login file. If you are using a different login-shell, edit your startup files manually Performance and special considerations The script siteconfig lapw is provided for general configuration and compilation of the WIEN2k package. When you call this script for the first time and follow the suggested answers, WIEN2k should run on your system (see ). The codes in the individual subdirectories /SRC program are compiled using make. The file Makefile is generated during installation using Makefile.orig as template. In some directories the source files *.frc, *.F and param.inc r/c contain both, the real and complex (for systems without inversion symmetry) version of the code. You create the coresponding versions with make and make complex, respectively. (The *.frc and *.F files will then be preprocessed automatically). The fine-grained parallel versions lapw0 mpi; lapw1 mpi, lapw1c mpi, lapw2 mpi, lapw2c mpi are created using make para (lapw0) and make rp; make cp.

232 214 CHAPTER 11. INSTALLATION AND DIMENSIONING For timing purposes a subroutine CPUTIM is used in several programs and specific routines for IBM-AIX, HP-UX, DEC-OSF1, SGI and SUN are available. On other systems cputim generic.c should work. Most of the CPU time will be spent in lapw1 and (to a smaller extent) in lapw2 and lapw0. Therefore we recommend to optimize the performance for these 3 programs: Find out which compiler options (man name of compiler ) make these programs run faster. You could specify a higher optimization (-O3), or specify a particular processor architecture (-qarch=pwr5 or -R10000,...). Good performance depends on highly optimized BLAS (and much less on LAPACK) libraries. Whenever possible, replace the supplied libraries (SRC lib/blas lapw SRC lib/lapack lapw), by routines from your vendor (mkl for Intel or AMD processors, aclm for AMD, essl for IBM, sunperf for SUN, complib.sgimath on SGI,...). Because of the superior performance of the Intel-mkl library we recommend ifort/mkl instead of gfortan (or some other commercial f90 compiler). If such libraries are not available use the GOTO-library (http://www.tacc.utexas.edu/tacc-projects/gotoblas2/). (Eventually you may try to optimize them yourself using the ATLAS system (see but this is no longer recommended. We provide an old ATLAS-BLAS for a Pentium3 with WIEN2k Global dimensioning parameters WIEN2k is written in Fortran 90 and all important arrays are allocated dynamically. The only important parameters left are NMATMAX and NUME, specifying the maximum matrixsize (should be adjusted to the memory of your hardware, see above) and the maximum number of eigenvalues (must be increased for unitcells with large number of electrons) Some less important parameters are still present and described in chapter dimensioning parameters of the respective section in chapter 6. We recommend to use siteconfig lapw for redimensioning and recompilation. In order to work properly, the parameter XXXX in the respective param.inc files must obey the following syntax: PARAMETER(XXXX=...) Note: between (, XXXX and = there must be no space Installation and Configuration of w2web General issues w2web requires perl, which should be available on most systems. (If not contact your system administrator or install it yourself from the WWW) When you start w2web for the first time on the computer where you want to execute WIEN2k (you may have to telnet, ssh,.. to this machine) with the command w2web [-p xxxx], you will be asked for a username/password (I recommend you use the same as for your UNIX login). You must also specify a port number (which can be changed the next time you start w2web). If the default port (7890) used to serve the interface is already in use by some other process, you will get the error message w2web failed to bind port port already in use!.

233 11.3. W2WEB 215 Then you will have to choose a different port number (between 1024 and 65536). Please remember this port number, you need it when connecting to the w2web server. Note: Only user root can specify port numbers below 1024! Once w2webhas been started, use your favorite WWW-browser to connect to w2web, specifying the correct portnumber, e.g. firefox where w2web runs:7890 On certain sites a firewall may block all high ports and one cannot connect to this machine. In these cases you can create a ssh-tunnel using the following commands: At your local host (the PC in front of you) connect to the w2web host (where you started w2web) using ssh -fnl 2000:w2web_host:7890 On your local host use a web browser and connect with: firefox Using Configuration you can further tailor the behaviour according to your wishes. In particular you can define new execution types to adjust to your queuing system. For example the line batch=batch < %f defines an execution type batch using the UNIX batch command. (w2web collects its commands in a temporary script and you can access it using %f). If you run on a machine with a queuing system (like loadleveler, sun-grid-engine, or pbs) you may define an execution type qsub=cat %f > w2web-job;qsub-wienjob_lapw The following scripts may serve as templates: qsub-wienjob lapw in $WIENROOT needs a master-job-template qsub-job0 lapw and examples for loadleveler and SGE are provided in $WIENROOT (you may need to adapt them! Other examples you can find on our FAQ-page on the web). Of course, with some small modifications you can define several execution types with eg. different number of processors or mpi vs. k-point parallel runs,... w2web saves several variables in startup files which are in the ( /.w2web) directory How does w2web work? w2web acts like a normal web-server - except that it runs on a user level port instead of the default http-port 80. It serves html-files and executes perl-scripts or executes system or user commands on the server host w2web-files in you home directory w2web creates on the first start of w2web on host hostname the directory.w2web/hostname in your home directory with the following content:.w2web/hostname/conf.w2web/hostname/logs.w2web/hostname/sessions

234 216 CHAPTER 11. INSTALLATION AND DIMENSIONING The configuration file conf/w2web.conf In this file various configuration parameters are stored by w2web. To restrict the access to certain IP addresses you can add lines like: deny=*.*.*.* allow= * The password file conf/w2web.users This file is created during the first run of w2web. If you remove this file, the next start of w2webwill activate the installation procedure again Using the https-protocol with w2web In order to use the https-protocol the perl-library Net::SSLeay in addition to the OpenSSL package must be installed on your system. Both are freely available. Then you must include a line with ssl=1 in w2web.conf. If you run w2web-server in ssl-mode you need a site certificate for your server. You may use the supplied certificate in $WIENROOT/SRC w2web/bin/w2web.pem (copy this file to your conf-directory and set the keyfile= /.w2web/<hostname>/conf/w2web.pem line in your w2web.conf). This certificate will not expire until 2015, but usually browsers will complain that they do not know the Certificate Authority who issued this certificate - if you don t like this message, you must buy a certificate from VeriSign, Thawte or a similar CA. Of course you must connect to https: instead of i.e. use: netscape https://hostname where w2web runs: Environment Variables WIEN2k uses the following environment variables: WIENROOT base directory where WIEN2k is installed PDFREADER specifies program to read pdf files (acroread, xpdf,...) SCRATCH directory where case.vector and case.help?? are stored. On slow NFS-filesystems, a local scratch-directory could greatly enhance the performance. EDITOR path and name of your prefered editor STRUCTEDIT PATH path where the structeditor tool is located OCTAVE PATH path where the structeditor tool is located OCTAVE EXEC PATH path where octave looks for executables (structeditor) XCRYSDEN TOPDIR if this variable is set WIEN2k will activate all interface extensions to XCrysDen. USE REMOTE [0 1] determines whether parallel jobs are run in background (on shared memory machines) or using rsh. It is overridden by settings in $WIENROOT/parallel options MPI REMOTE [0 1] determines whether the mpirun command is issued on the master-node, or first an ssh to a remote node is done and there the mpirun command is issued. Usually, on many mpi-2 systems the first method is preferred, on mpi-1 the second.

235 11.4. ENVIRONMENT VARIABLES 217 WIEN GRANULARITY Default granularity for parallel execution. It is overridden by setting the granularity in the.machines file or in $WIENROOT/parallel options WIEN EXTRAFINE if set, the residual k-points are spread one by one over the processors. TASKSET [no command] specifies an optional command for binding a process to a specific core (like: taskset -c) In addition on some systems variables like: LD LIBRARY PATH path to libraries of compiler and math-libs OMP NUM THREADS on multi-core machines for parallelization in certain libraries (mkl, goto)

236 218 CHAPTER 11. INSTALLATION AND DIMENSIONING

237 12 Trouble shooting In this chapter hints are given for solving some difficulties that have occurred frequently. This chapter is by no means complete and the authors would appreciate further suggestions which might be useful for other users. Beside the printed version of the users guide, an online pdf version is available using help lapw. You can search for a specific keyword (use f keyword) and hopefully find some information. There is a mailing list for WIEN2k related questions. To subscribe to this list goto: and subscribe. You will then automatically be added to the mailing list and can post questions. Please make use of this list! If an error occurs in one of the SCF programs, a file program.error is created and an error message is printed into these files. The run lapw script checks for these files and will automatically stop if a non-empty error file occurs. Check the files case.dayfile (which is written by init lapw and run lapw), :log (where a history of all commands using x is given) and *.error for possible explanations. In several places the dimensions are checked. The programs print a descriptive error message and stop. case.outputnn: This file gives error messages if the atomic spheres overlap. But it should also be used to check the distances between the atoms and the coordination number (same distance). If inconsistencies exists, your case.struct file may contain an error. A check for overlapping spheres is also included in mixer and lapw1. case.outputd: Possible stops or warnings are: NO SYMMETRY OPERATION FOUND IN ROTDEF : This indicates that in your case.struct file either the positions of equivalent atoms are not specified correctly (only positive coordinates allowed!!) or the symmetry operations are wrong. case.output1: Possible stops or warnings are: NO ENERGY LIMITS FOUND IN SELECT : This indicates that E top or E bottom could not be found for some u l (r, E l ). Check your input if it happens in the zeroth iteration. Later, (usually in the second to sixth iteration) it may indicate that in your SCF cycle something went wrong and you are using a crazy potential. Usually it means that mixing of the charge densities was diverging and large charge fluctuations occured. Check previous charges for being physically reasonable (grep for labels :NTOxx :CTOxx :DIS :NEC01). Usually this happens when your input is not ok, or for very ill 219

238 220 CHAPTER 12. TROUBLE SHOOTING conditioned problems (very rare), or more likely, when Ghostbands appeared (or some states were missing) because of bad energy parameters in case.in1. You will probably have to delete case.broy* and case.scf, rerun x dstart and then change some calculational parameters. These could be: fixing some energy parameter (modify both, case.in1 and case.in1 orig or try the -in1orig switch if you have used -in1new); switch to a broadening method (TEMP with eg mry); or increase the k-mesh (magnetic metals); or reduce the mixing parameter in case.inm slightly (eg. to 0.1). In very difficult (magnetic) cases a PRATT mixing with eg mixing might be helpful at the beginning of the scf cycle (but later switch to MSEC1 again)! STOP RDC 22 : This indicates that the overlap matrix is not positive definite. This usually happens if your case.struct file has some error in the structure or if you have an (almost) linear dependent basis, which can happen for large RKMAX values and/or if you are using very different (extremely small and large) sphere radii R MT. X EIGENVALUES BELOW THE ENERGY emin : This indicates that X eigenvalues were found below emin. Emin is set in case.in1 (see sec ) or in case.klist generated by KGEN, see 6.3, 6.5). It may indicate that your value of emin is too high or the possibility of ghostbands, but it can also be intentional to truncate some of the low lying eigenvalues. If you don t find enough eigenvalues (e.g.: in a cell with 4 oxygens you expect 4 oxygen s bands at roughly -1 Ry) check the energy window (given at the end of the first k-point in case.in1 or in case.klist) and make sure your energy parameters are found by subroutine SELECT or set them by hand at a reasonable value. case.output2: Possible stops or warnings are: CANNOT BE FOUND : This warning, which could produce a very long output file, indicates that some reciprocal K-vector would be requested (through the k-vector list of lapw1), but was not present in the list of the K generated in lapw2. You may have to increase the NWAV, and/or KMAXx parameters in lapw2 or increase GMAX in case.in2. The problems could also arise from wrong symmetry operations or a wrong structure in case.struct. QTL-B VALUE : If larger than a few percent, this indicates the appearance of ghost bands, which are discussed below in section The few percent message (e.g up to 10 %) does not indicate a ghost band, but can happen e.g. in narrow d-bands, where the linearization reaches its limits. In these cases one can add a local orbital to improve the flexibility of the basis set. (Put one energy near the top and the other near the bottom of the valence band, see section 7.5.3). FERMI LEVEL not converged (or similar messages). This can have several reasons: i) Try a different Fermi-Method (change TETRA to GAUSS or TEMP in case.in2). ii) Count the number of eigenvalues in case.output1 and compare it with the number of valence electrons. If there are too few eigenvalues, either increase EMAX in case.klist (from 1.5 to e.g. 2.5) or check if your scf cycle had large charge oszillations (see SELECT error above) If the SCF cycle stops somewhere (especially in the first few iterations), it is quite possible, that the source of the error is actually in a previous part of the cycle or even in a previous (e.g. the zeroth) iteration. Check in the case.scf file previous charges, eigenvalues,... whether they are physically reasonable (see SELECT error above) Ghost bands Approximate linear dependence of the basis set or the linearization of the energy dependence of the radial wave functions (see section 2.2) can lead to spurious eigenvalues, termed ghost bands.

239 12.1. GHOST BANDS 221 The first case may occur in a system which has atoms with very different atomic sphere radii. Suppose you calculate a hydroxide with very short O-H bonds so that you select small R MT radii for O and H such as e.g. 1.0 and 0.6 a.u., respectively. The cation may be large and thus you could choose a large R MT of e.g. 2.4 a.u. However, this gives a four time larger effective RKmax for the cation than for H, (e.g when you select RKmax=4.0 in case.in1). This enormous difference in the convergence may lead to unphysical eigenvalues. In such cases choose lmax=12 in case.in1 (in order to get a very good re-expansion of the plane waves) and reduce R MT for the cation to e.g. 1.8 a.u. The second case can occur when you don t use a proper set of local orbitals. In this situation the energy region of interest (valence bands) falls about midway between two states with different principle quantum numbers, but with the same l-value (for one atom). Take for example Ti with its 3p states being occupied as (semi-core) states, while the 4p states remain mostly unoccupied. In the valence band region neither of those two states (Ti 3p, 4p) should appear. If one uses 0.2 Ry for the expansion energy E(1) for the p states of Ti, then Ti-p states do appear as ghost bands. Such a run is shown below for T io 2 (rutile). The lowest six eigenvalues at GAMMA fall between about and Ry. They are ghost bands derived from fictitious Ti-p states. The next four eigenvalues between and Ry correspond to states derived from O 2s states, which are ok, since there are four O s per unit cell, four states are found. The occurrence of such unphysical (indeed, unchemical!) ghostbands is the first warning that something went wrong. A more definite warning comes upon running LAPW2, where the corresponding charge densities are calculated. If the contribution to the charge density from the energy derivative of the basis function [the B lm coefficient in equ. 2.4,2.7] is significant (i.e. much more than 5 per cent) then a warning is issued in LAPW2. In the present example it reads: QTL-B VALUE.EQ !!!!!! This message is found in both the case.scf file and in case.output2. When such a message appears, one can also look at the partial charges (QTL), which are printed under these conditions to OUTPUT2, and always appear in the files case.helpxxx, etc., where the last digit refers to the atomic index. In the file below, note the E(1) energy parameter as well as the 6 ghost band energies around top of file:tio2.scf ATOMIC SPHERE DEPENDENT PARAMETERS FOR ATOM Titanium OVERALL ENERGY PARAMETER IS.2000 E( 0)= > E( 1)=.2000 E( 2)=.2000 E(BOTTOM)= E(TOP)= ATOMIC SPHERE DEPENDENT PARAMETERS FOR ATOM Oxygen OVERALL ENERGY PARAMETER IS.2000 E( 0)= E(BOTTOM)= E(TOP)=.670 K= :RKM : MATRIX SIZE= 599 RKM= 6.99 WEIGHT= 8.00 PGR: EIGENVALUES ARE: ******************************************************** NUMBER OF K-POINTS: 1

240 222 CHAPTER 12. TROUBLE SHOOTING :NOE : NUMBER OF ELECTRONS = :FER : F E R M I - ENERGY = :POS01: AT.NR. -1 POSITION = MULTIPLICITY= 2 LMMAX=10 LM= :CHA01: TOTAL CHARGE INSIDE SPHERE 1 = :PCS01: PARTIAL CHARGES SPHERE = 1 S,P,D,F,PX,PY,PZ,D-Z2,D-X2Y2,D-XY,D-XZ,D-YZ :QTL01: VXX VYY VZZ UP TO R :VZZ01: :POS02: AT.NR. -2 POSITION = MULTIPLICITY= 4 LMMAX=16 LM= :CHA02: TOTAL CHARGE INSIDE SPHERE 2 = :PCS02: PARTIAL CHARGES SPHERE = 2 S,P,D,F,PX,PY,PZ,D-Z2,D-X2Y2,D-XY,D-XZ,D-YZ :QTL02: VXX VYY VZZ UP TO R :VZZ02: :CHA : TOTAL CHARGE INSIDE CELL = :SUM : SUM OF EIGENVALUES = QTL-B VALUE.EQ !!!!!! NBAND in QTL-file: end of truncated file tio2.scf Next we show tio2.output2 for the first of the ghost bands at Ry. One sees that it corresponds mainly to a p-like charge, which originates from the energy derivative part Q(UE) of the Kohn-Sham orbital. Q(UE) contributes 40.1% compared with 8.5% from the main component Q(U). Q(UE) greater than Q(U) is a good indication for a ghost band part of file tio2.output QTL-B VALUE.EQ !!!!!! K-POINT: BAND # 1 E= WEIGHT= L= 0 L= 1 PX: PY: PZ: L= 2 DZ2: DX2Y2: DXY: DXZ: DYZ: L= 3 QINSID: Q(U) : Q(UE) : L= 0 L= 1 PX: PY: PZ: L= 2 DZ2: DX2Y2: DXY: DXZ: DYZ: L= 3 QINSID: Q(U) : Q(UE) : QOUT : bottom of truncated file Another file in which the same information can be found is tio2.help031, since the ghost band is caused by a bad choice for the Ti-p energy parameter: Top of file tio2.help K-POINT: BAND # 1 E= WEIGHT= L= L= PX: PY: PZ: L= DZ2: DX2Y2: DXY: DXZ: DYZ: L= L= L= L= bottom of truncated file Note again for L=1 the percentage of charge associated with the primary (APW) basis functions ul (8.5%) versus that coming from the energy derivative component (40.1%).

241 12.1. GHOST BANDS 223 If a ghost band appears, one should first analyze its origin as indicated above, then use appropriate local orbitals to improve the calculation and get rid of these unphysical states. Do not perform calculations with ghost-bands, even when the calculation converges. Good luck!

242 224 CHAPTER 12. TROUBLE SHOOTING

243 13 References Abt R., Ambrosch-Draxl C. and Knoll P Physica B Abt R PhD Theses, Univ.Graz Ahmed S.J., Kivinen J., Zaporzan B., Curiel L., Pichardo S. and Rubel O Comp. Phys. Commun. 184, Andersen O.K Solid State Commun. 13, Phys. Rev. B 12, 3060 Ambrosch-Draxl C., Blaha P., and Schwarz K Phys.Rev. B44, 5141 Ambrosch-Draxl C., Majewski J. A., Vogl P., and Leising G. 1995, PRB Ambrosch-Draxl C. and Sofo J., 2006 Comp. Phys. Comm. 175, 1 V.I. Anisimov, I.V. Solovyev, M.A. Korotin, M.T. Czyzyk, and G.A. Sawatzky, Phys. Rev. B 48, (1993). V.I. Anisimov, J. Zaanen, and O.K. Andersen, Phys. Rev. B 44, 943 (1991) Bader R. F. W. 2001: Blaha P. and Schwarz K Int. J. Quantum Chem. XXIII, 1535 Blaha P., Schwarz K., and Herzig P 1985 Phys. Rev. Lett. 54, 1192 Blaha P., Schwarz K., and Dederichs P 1988 Phys. Rev B 38, 9368 Blaha P., Schwarz K., Sorantin P.I. and Trickey S.B Comp. Phys. Commun. 59, 399 Blaha P., Sorantin P.I., Schwarz K and Singh D Phys. Rev. B 46, 1321 Blaha P., Hofstätter H., Koch R., Laskowski R. and Schwarz K. 2009, J.Comput.Phys. 229, 453. Blöchl P.E., Jepsen O. and Andersen O.K. 1994, Phys. Rev B 49, Boettger J.C. and Albers R.C Phys. Rev. B 39, 3010 Boettger J.C. and Trickey S.B Phys. Rev. B 29, 6425 Brooks M.S.S Physica B 130, 6 Charpin, T (see $WIENROOT/SRC/elast-UG.ps) Czyzyk M.T. and G.A. Sawatzky, Phys. Rev. B 49, (1994). 225

244 226 CHAPTER 13. REFERENCES Desclaux J.P Comp. Phys. Commun. 1, 216; note that the actual code we use is an apparently unpublished relativistic version of the non-relativistic code described in this paper. Though this code is widely circulated, we have been unable to find a formal reference for it Comp. Phys. Commun. 9, 31; this paper contains much of the Dirac-Fock treatment used in Desclaux s relativistic LSDA code. O. Eriksson, B. Johansson, and M.S.S. Brooks, J. Phys. C 1, 4005 (1989) Feldman J.L., Mehl M.J., and Krakauer H Phys. Rev. B 35, 6395 Gay David M., ALGORITHM 611 Subroutines for Unconstrained Minimization Using a Model/Trust-Region Approach, ACM Trans. Math. Software 9 (1983), pp Grimme S., Antony J., Ehrlich, S. and Krieg, H J. Chem. Phys. 132, Haas P., Tran F., Blaha P., Schwarz K. 2011, Phys.Rev. B 83, Hébert-Souche C., Louf P.-H., Blaha P., M. Nelhiebel, Luitz J., Schattschneider P., Schwarz K. and Jouffrey B.; The orientation dependent simulation of ELNES, Ultramicroscopy, 83, 9 (2000) L.L. Hirst, Rev. Mod. Phys. 69, 607 (1997) Hohenberg P. and Kohn W Phys. Rev. 136, B864 International Tables for X-Ray Crystallography 1964 Vol.1; The Kynoch Press, Birmingham UK Jansen H.J.F. and Freeman A.J Phys. Rev. B 30, Phys. Rev. B 33, 8629 King-Smith R.D., Vanderbilt D Phys. Rev. B 47, 1651 Koelling D.D J. Phys. Chem. Solids 33, 1335 Koelling D.D. and Arbman G.O J.Phys. F: Met. Phys. 5, 2041 Koelling D.D. and Harmon B.N J. Phys. C: Sol. St. Phys. 10, 3107 Kohler B., Wilke S., Scheffler M., Kouba R. and Ambrosch-Draxl C Comp.Phys.Commun. 94, 31 Kohn W. and Sham L.J Phys. Rev. 140, A1133 Kokalj A J.Mol.Graphics and Modelling 17, 176 Koller D., Tran F. and Blaha P Phys. Rev. B 85, Krimmel H.G., Ehmann J., Elsässer C., Fähnle M. and Soler J.M. 1994, Phys.Rev. B50, 8846 Kuneš J, Novák P., Schmid R., Blaha P. and Schwarz K. 2001, Phys. Rev. B64, Kara, M. and Kurki-Suonio K Acta Cryst A37, 201 Laskowski R. and Blaha P. 2012a, Phys. Rev. B 85, Laskowski R. and Blaha P. 2012b, Phys. Rev. B 85, Laskowski R., Blaha P., and Tran F. 2013, Phys. Rev. B 87,

245 227 Liberman D., Waber J.T., and Cromer D.T. 1965, Phys. Rev. 137A, 27 A.I. Liechtenstein, V. I. Anisimov, J. Zaanen, Phys. Rev. B 52, R5467 (1995) Luitz J., Maier M., Hébert C., Schattschneider P., Blaha P., Schwarz K., Jouffrey B Eur. Phys J. B 21, MacDonald A. H., Pickett, W. E. and Koelling, D. D J. Phys. C 13, 2675 Madsen G. K. H., Blaha P, Schwarz K, Sjöstedt E and Nordström L 2001, Phys. Rev. B64, Marks L. D., and Luke R. 2008, Phys. Rev. B 78, Marks L. D. 2013, J. Chem. Theory Comput., 9, 2786 Mattheiss L.F. and Hamann D.R Phys. Rev. B 33, 823 Mattsson A., Armiento R., Paier J., Kresse G., Wills J. and Mattsson T 2008 J. Chem. Phys. 128, Meyer-ter-Vehn J. and Zittel W Phys. Rev. B37, 8674 Moruzzi V.L., Janak J.F., and Williams A.R Calculated Properties of Metals (Pergamon, NY) Murnaghan F.D., Proc.Natl.Acad.Sci. USA 30, 244 (1944) Neckel A., Schwarz K., Eibler R. and Rastl P Microchim.Acta, Suppl.6, 257 Nelhiebel M., Louf P. H., Schattschneider P., Blaha P., Schwarz K. and Jouffrey B.; Theory of orientation sensitive near-edge fine structure core-level spectroscopy, Phys.Rev. B59, (1999) Novak P see $WIENROOT/SRC/novak lecture on spinorbit.ps Novák P., Boucher F., Gressier P., Blaha P. and Schwarz K Phys. Rev. B 63, Novák P see $WIENROOT/SRC/novak lecture on ldaumatrixelements.ps and Novak P see $WIENROOT/SRC/Bhf 3.ps and Paier J., Marsman M., Hummer K., Kresse G., Gerber I. C. and Ángyán J. G., J. Chem. Phys. 124, (2006) Ortenzi L., Mazin I., Blaha P. and Boeri L. 2012, Phys. Rev. B (in print) Pardini L., Bellini V., Manghi F. and Ambrosch-Draxl C. 2011, Comp.Phys.Commun. 183, 628 (2012) Perdew J.P, Chevary J.A., Vosko S.H., Jackson K.A., Pederson M.R., Singh D.J., and Fiolhais C Phys.Rev.B46, 6671 Perdew J.P. and Wang Y. 1992, Phys.Rev. B45, Perdew J.P., Burke S. and Ernzerhof M. 1996, Phys.Rev.Let. 77, 3865 Perdew J.P., Kurth S., Zupan J. and Blaha P. 1999, Phys.Rev.Let. 82, 2544 Perdew J.P. et al. 2008, Phys. Rev. Let. 100,

246 228 CHAPTER 13. REFERENCES Perdew,J.P. et al., 2009, Phys. Rev. Lett. 103, and 106, (E) (2011). Pratt G.W Phys. Rev. 88, 1217 Ray A.K. and Trickey S.B Phys. Rev. B24, 1751; erratum 1983, Phys. Rev. B28, 7352 Reshak A. and Jamal M. 2013, J. Alloys and Compounds, 555, 362 Resta R., Posternak M. and Baldereschi A Phys. Rev. Lett. 70, 1010 Rondinelli JM, Beng Bin and Marks LD. 2007, Comp. Mater. Sci. 40, (also: Los Alamos archive, physics/ (http://xxx.lanl.gov/abs/physics/ ) Schwarz K., Neckel A and Nordgren J, J.Phys.F:Metal Phys. 9, 2509 (1979) Schwarz K., and Wimmer E, J.Phys.F:Metal Phys. 10, 1001 (1980) Schwarz K. and Blaha P.: Lecture Notes in Chemistry 67, 139 (1996) Schwarz K., P.Blaha and Madsen, G. K. H. Comp.Phys.Commun. 147, 71 (2002) Singh D., Krakauer H., and Wang C.-S Phys. Rev. B34, 8391 Singh, D Phys. Rev. B40, 5428 Singh D. 1991, Phys.Rev. B43, 6388 Singh D. and Nordström L 2006, Plane waves, pseudopotentials and the LAPW method, 2 nd edition, Springer, New York Sjöstedt E, Nordström L and Singh D. J Solid State Commun. 114, 15 Sofo J and Fuhr J 2001: $WIENROOT/SRC/aim sofo notes.ps Soler J.M. and Williams A.R. 1989, Phys.Rev. B40, 1560 Sorantin P.I., and Schwarz K.H. 1992, Inorg.Chem. 31, 567 Stahn J, Pietsch U, Blaha P and Schwarz K. 2001, Phys.Rev. B63, Sun J., Xiao B., Fang Y., Haunschild R., Hao P., Ruzsinszky A., Csonka G., Scuseria G., Perdew J Phys Rev. Lett. 111, Tao Jianmin, Perdew J.P., Staroverov V. and Scuseria G. 2003, Phys.Rev.Let. 91, Tran F, Blaha P Schwarz K and Novak P 2006, Phys. Rev. B 74, Tran F, Laskowski R, Blaha P and Schwarz K. 2007, Phys. Rev. B 75, Tran F and Blaha P 2009, Phys. Rev. Lett. 102, Tran F, Blaha P 2011, Phys. Rev. B 83, Tran F 2012 Phys. Lett. A (in press) von Barth U. and Hedin L J. Phys. C.: Sol. St. Phys. 5, 1629 Wei S.H., Krakauer H., and Weinert M Phys. Rev. B 32, 7792 Weinert M J. Math. Phys. 22, 2433 Weinert M., Wimmer E., and Freeman A.J Phys. Rev. B26, 4571 Wimmer E., Krakauer H., Weinert M., and Freeman A.J Phys. Rev. B24, 864

247 229 Wu Z., Cohen R., 2006 Phys. Rev. B73, Yanchitsky B. and Timoshevskii T. 2001, Comp.Phys.Commun. 139, 235 Yu R., Singh D. and Krakauer H. 1991, Phys.Rev. B43, 6411

248 230 CHAPTER 13. REFERENCES

249 Part IV Appendix 231

250

251 A Local rotation matrices Local rotation matrices are used to rotate the global coordinate system (given by the definition of the Bravais matrix) to a local coordinate system for each atomic site. They are used in the program for two reasons: to minimize the number of LM combinations in the lattice harmonics expansion (of potential and charge density according to equ. 2.10). For example for point group mm2 one needs for L=1 just LM=1,0 if the coordinate system is chosen such that the z-axis coincides with the 2-fold rotation axis, while in an arbitrary coordinate system the three terms 1,0; 1,1 and -1,1 are needed (and so on for higher L). The interpretation e.g. of the partial charges requires a proper orientation of the coordinate system. In the example given above, the p orbitals split into 2 irreducible representations, but they can be attributed to p z and p x, p y only if the z-axis is the 2-fold rotation axis. It is of course possible to perform calculations without local rotation matrices, but in such a case the LM combinations given in Table 7.51 (and by SYMMETRY) may not be correct. (The LM values for arbitrary orientations may be obtained from a procedure described in Singh 94.) Fortunately, the local rotation matrices are usually fairly simple and are now automatically inserted into your case.struct file. Nevertheless we recommend to check them in order to be sure. The most common coordinate transformations are interchanging of two axes (e.g. x and z) rotation by 45 (e.g. in the xy-plane) rotation of z into the (111) direction Inspection of the output of SYMMETRY tells you if the local rotation matrix is the unit matrix or it gives you a clear indication how to find the proper matrix. The local rotation matrix R, which transforms the global coordinates r to the rotated ones r, is defined by Rr = r. There are two simple ways to check the local rotation matrixes together with the selected LM combinations: charge density plots generated with LAPW5 must be continuous across the atomic sphere boundary (especially valence or difference density plots are very sensitive, see 8.13) Perform a run of LAPW1 and LAPW2 using the GAMMA-point only (or a complete star of another k point). In such a case, wrong LM combinations must vanish. Note that the latter is true only in this case. For a k mesh in the IBZ wrong LM combinations do not vanish and thus must be omitted!! A first example for local rotation matrices is given for the rutile TiO2, which has already been described as an example in section Also two other examples will be given (see below). 233

252 234 APPENDIX A. LOCAL ROTATION MATRICES A.1 Rutile (T io 2 ) Examine the output from symmetry. It should be obvious that you need local rotation matrices for both, Ti and O:... Titanium operation # 1 1 Titanium operation # 2-1 Titanium operation # 5 2 z Titanium operation # 6 m n z Titanium operation # 12 m n 110 Titanium operation # 13 m n -110 Titanium operation # Titanium operation # pointgroup is mmm (neg. iatnr!!) axes should be: m n z, m n y, m n x This output tells you, that for Ti a mirror plan normal to z is present, but the mirror planes normal to x and y are missing. Instead, they are normal to the (110) plane and thus you need to rotate x, y by 45 around the z axis. (The required choice of the coordinate system for mmm symmetry is also given in Table 7.51)... Oxygen operation # 1 1 Oxygen operation # 6 m n z Oxygen operation # 13 m n -110 Oxygen operation # pointgroup is mm2 (neg. iatnr!!) axes should be: 2 z, m n y For O the 2-fold symmetry axes points into the (110) direction instead of z. The appropriate rotation matrices for Ti and O are: A.2 Si Γ-phonon Si possesses a face-centered cubic structure with two equivalent atoms per unit cell, at (±0.125, ±0.125, ±0.125). The site symmetry is -43m. For the Γ-phnon the two atoms are displaced in opposite direction along the (111) direction and cubic symmetry is lost. The output of SYMMETRY gives the following information: Si operation # 1 1 Si operation # 13 m n -110 Si operation # 16 m n -101 Si operation # 17 m n 0-11 Si operation # Si operation # pointgroup is 3m (neg. iatnr!!) axis should be: 3 z, m n y lm:

253 A.3. TRIGONAL SELENIUM 235 Therefore the required local rotation matrix should rotate z into the (111) direction and thus the matrix in the struct file should be: A.3 Trigonal Selenium Selenium possesses space group P3121 with the following struct file: H LATTICE,NONEQUIV.ATOMS: 1 MODE OF CALC=RELA POINTGROUP: ATOM= -1: X= Y= Z= MULT= 3 ISPLIT= 8 ATOM= -1: X= Y= Z= ATOM= -1: X= Y= Z= Se NPT= 381 R0= RMT= Z:34.0 LOCAL ROT.MATRIX: IORD OF GROUP G0... The output of SYMMETRY reads: Se operation # 1 1 Se operation # 9 2 $ $$ $ 110 pointgroup is 2 (neg. iatnr!!) axis should be: 2 z lm: Point group 2 should have its 2-fold rotation axis along z, so the local rotation matrix can be constructed in two steps: firstly interchange x and z (that leads to z (011) ) and secondly rotate from (011) into (001) (see the struct file given above). Since this is a hexagonal lattice, SYMMETRY uses the hexagonal axes, but the local rotation matrix must be given in cartesian coordinates.

254 236 APPENDIX A. LOCAL ROTATION MATRICES

255 B Periodic Table 237

256 238 APPENDIX B. PERIODIC TABLE

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